# zbMATH — the first resource for mathematics

## Liu, Chun

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 Author ID: liu.chun Published as: Liu, C.; Liu, Chun
 Documents Indexed: 158 Publications since 1987, including 2 Books
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#### Co-Authors

 1 single-authored 14 Shen, Jie 12 Du, Qiang 9 Calderer, Maria-Carme T. 9 Hyon, Yunkyong 8 Feng, James J. 8 Lin, Fang Hua 7 Wang, Xiaoqiang 7 Yue, Xingye 6 Ryham, Rolf J. 6 Xu, Shixin 6 Yue, Pengtao 5 Lin, Taichia 5 Yang, Xiaofeng 4 Walkington, Noel J. 4 Wu, Hao 3 Chen, Minxin 3 Duan, Chenghua 3 Eisenberg, Bob 3 Giga, Yoshikazu 3 Jiang, Bin 3 Lai, Mingjun 3 Lee, Hijin 3 Lin, Ping 3 Liu, Lishan 3 Liu, Pei 3 Sheng, Ping 3 Tan, Zhong 3 Wang, Cheng 3 Wenston, Paul R. 3 Xu, Jinchao 3 Xu, Xiang 3 Zhang, Ke 2 Brannick, James J. 2 Forest, M. Gregory 2 Hsieh, Chia-Yu 2 Huang, Tao 2 Koba, Hajime 2 Lee, Chiun-Chang 2 Lei, Zhen 2 Li, Shuwang 2 Li, Xiantao 2 Lu, Min-Jhe 2 Ma, Lina 2 Ma, Tianbao 2 Majd, Sheereen 2 Ning, Jianguo 2 Qian, Tiezheng 2 Sato, Norifumi 2 Schlömerkemper, Anja 2 Sun, Huan 2 Sun, Pengtao 2 Tonegawa, Yoshihiro 2 Voss, Karl 2 Wang, Qi 2 Wang, Yong 2 Wu, Yonghong 2 Yu, Peng 2 Zhang, Ping 2 Zhou, Yi 2 Zikatanov, Ludmil T. 1 Adler, James H. 1 Alvarez, Sergio A. 1 Ambrosi, Davide 1 Baek, Seungik 1 Bauman, Patricia E. 1 Belmonte, Andrew 1 Benešová, Barbora 1 Carrillo de la Plata, José Antonio 1 Chan, Christina K. 1 Chen, Falai 1 Chen, Geng 1 Chen, Gui-Qiang G. 1 Chen, Xinfu 1 Cheng, Qing 1 De Anna, Francesco 1 deForest, Russ 1 Deng, Chao 1 Ding, Xiao-yu 1 Du, Yi 1 Eisenberg, Robert S. 1 Endo, Masakazu 1 Fang, Daoyuan 1 Feng, Xiaobing 1 Fonseca, James E. 1 Forster, Johannes 1 García-Cervera, Carlos J. 1 Gharahi, Hamidreza 1 Golovaty, Dmitry 1 Götz, Dario 1 Gou, Kun 1 Guo, Limin 1 Hao, Wenrui 1 He, Yinnian 1 Hou, Thomas Yizhao 1 Hua, Jinsong 1 Jiang, Feng 1 Jiang, Jie 1 Jifara, Worku 1 Kim, Jungsil 1 Kinderlehrer, David ...and 57 more Co-Authors
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#### Serials

 13 Journal of Computational Physics 10 Communications in Mathematical Sciences 9 Archive for Rational Mechanics and Analysis 6 Discrete and Continuous Dynamical Systems 5 SIAM Journal on Mathematical Analysis 5 Discrete and Continuous Dynamical Systems. Series B 4 Journal of Differential Equations 4 Physica D 3 Communications on Pure and Applied Mathematics 3 SIAM Journal on Numerical Analysis 3 SIAM Journal on Applied Mathematics 3 Multiscale Modeling & Simulation 3 Communications in Computational Physics 2 Applicable Analysis 2 International Journal of Engineering Science 2 Journal of Fluid Mechanics 2 Mathematical Methods in the Applied Sciences 2 Nonlinearity 2 Quarterly of Applied Mathematics 2 Journal of Non-Newtonian Fluid Mechanics 2 Physics of Fluids 2 Interfaces and Free Boundaries 2 Oberwolfach Reports 2 Series in Contemporary Applied Mathematics CAM 2 Numerical Mathematics: Theory, Methods and Applications 2 Journal of Nonlinear Science and Applications 2 Computational and Mathematical Biophysics 1 Modern Physics Letters A 1 Computer Methods in Applied Mechanics and Engineering 1 Discrete Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Mathematics of Computation 1 Bulletin of Mathematical Biology 1 BIT 1 Journal of Functional Analysis 1 Acta Scientiarum Naturalium Universitatis Sunyatseni 1 Circuits, Systems, and Signal Processing 1 Numerical Methods for Partial Differential Equations 1 Journal of Scientific Computing 1 Economics Letters 1 Differential and Integral Equations 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Journal of Elasticity 1 Journal of Partial Differential Equations 1 Continuum Mechanics and Thermodynamics 1 Calculus of Variations and Partial Differential Equations 1 Journal of Mathematical Fluid Mechanics 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Journal of High Energy Physics 1 JP Journal of Algebra, Number Theory and Applications 1 Communications on Pure and Applied Analysis 1 Journal of Applied Mathematics and Computing 1 Transactions of Beijing Institute of Technology 1 Chinese Journal of Computational Mechanics 1 Journal of Hefei University of Technology. Natural Science 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Progress of Theoretical Physics. Supplement 1 Acta Mathematica Sinica. Chinese Series 1 Kinetic and Related Models 1 Journal of Computer Applications 1 Communications in Theoretical Physics 1 Molecular Based Mathematical Biology 1 International Journal of Systems Science. Principles and Applications of Systems and Integration 1 Annals of Mathematical Sciences and Applications 1 IEEE Transactions on Control of Network Systems
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#### Fields

 90 Fluid mechanics (76-XX) 62 Partial differential equations (35-XX) 32 Numerical analysis (65-XX) 27 Statistical mechanics, structure of matter (82-XX) 19 Mechanics of deformable solids (74-XX) 18 Biology and other natural sciences (92-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 5 General and overarching topics; collections (00-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Operator theory (47-XX) 4 Optics, electromagnetic theory (78-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Differential geometry (53-XX) 3 Quantum theory (81-XX) 3 Systems theory; control (93-XX) 2 Ordinary differential equations (34-XX) 2 Manifolds and cell complexes (57-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Probability theory and stochastic processes (60-XX) 2 Computer science (68-XX) 2 Information and communication theory, circuits (94-XX) 1 Group theory and generalizations (20-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Statistics (62-XX) 1 Relativity and gravitational theory (83-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematics education (97-XX)

#### Citations contained in zbMATH

114 Publications have been cited 2,675 times in 1,321 Documents Cited by Year
Nonparabolic dissipative systems modeling the flow of liquid crystals. Zbl 0842.35084
Lin, Fang-Hua; Liu, Chun
1995
A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method. Zbl 1092.76069
Liu, Chun; Shen, Jie
2003
A diffuse-interface method for simulating two-phase flows of complex fluids. Zbl 1130.76437
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
2004
On hydrodynamics of viscoelastic fluids. Zbl 1076.76006
Lin, Fang-Hua; Liu, Chun; Zhang, Ping
2005
Existence of solutions for the Ericksen-Leslie system. Zbl 0963.35158
Lin, Fang-Hua; Liu, Chun
2000
A phase field approach in the numerical study of the elastic bending energy for vesicle membranes. Zbl 1116.74384
Du, Qiang; Liu, Chun; Wang, Xiaoqiang
2004
Global solutions for incompressible viscoelastic fluids. Zbl 1138.76017
Lei, Zhen; Liu, Chun; Zhou, Yi
2008
Preconditioned multigrid methods for unsteady incompressible flows. Zbl 0908.76064
Liu, C.; Zheng, X.; Sung, C. H.
1998
Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method. Zbl 1158.76319
Yang, Xiaofeng; Feng, James J.; Liu, Chun; Shen, Jie
2006
An Eulerian description of fluids containing viscoelastic particles. Zbl 1009.76093
Liu, Chun; Walkington, Noel J.
2001
Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions. Zbl 1086.74024
Du, Qiang; Liu, Chun; Wang, Xiaoqiang
2006
Partial regularity of the dynamic system modeling the flow of liquid crystals. Zbl 0948.35098
Lin, Fang-Hua; Liu, Chun
1996
On energetic variational approaches in modeling the nematic liquid crystal flows. Zbl 1156.76007
Sun, Huan; Liu, Chun
2009
Static and dynamic theories of liquid crystals. Zbl 1433.82014
Lin, Fanghua; Liu, Chun
2001
A phase field formulation of the Willmore problem. Zbl 1125.35366
Du, Qiang; Liu, Chun; Ryham, Rolf; Wang, Xiaoqiang
2005
Approximation of liquid crystal flows. Zbl 1040.76036
Liu, Chun; Walkington, Noel J.
2000
Analysis of a phase field Navier-Stokes vesicle-fluid interaction model. Zbl 1172.74016
Du, Qiang; Li, Manlin; Liu, Chun
2007
Global existence for a 2D incompressible viscoelastic model with small strain. Zbl 1132.76008
Lei, Zhen; Liu, Chun; Zhou, Yi
2007
On the general Ericksen-Leslie system: Parodi’s relation, well-posedness and stability. Zbl 1320.76010
Wu, Hao; Xu, Xiang; Liu, Chun
2013
Analysis of finite element approximations of a phase field model for two-phase fluids. Zbl 1111.76028
Feng, Xiaobing; He, Yinnian; Liu, Chun
2007
A mathematical model for the hard sphere repulsion in ionic solutions. Zbl 1406.76089
Hyon, Yunkyong; Eisenberg, Bob; Liu, Chun
2011
Energetic variational approaches in modeling vesicle and fluid interactions. Zbl 1183.74056
Du, Qiang; Liu, Chun; Ryham, Rolf; Wang, Xiaoqiang
2009
Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids. Zbl 1195.76120
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
2005
An energy law preserving $$C^0$$ finite element scheme for simulating the kinematic effects in liquid crystal dynamics. Zbl 1133.65077
Lin, Ping; Liu, Chun; Zhang, Hui
2007
On a micro-macro model for polymeric fluids near equilibrium. Zbl 1113.76017
Lin, Fang-Hua; Liu, Chun; Zhang, Ping
2007
Energetic variational approach in complex fluids: maximum dissipation principle. Zbl 1423.76380
Hyon, Yunkyong; Kwak, Do Young; Liu, Chun
2010
Viscoelastic effects on drop deformation in steady shear. Zbl 1082.76007
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
2005
An energetic variational formulation with phase field methods for interfacial dynamics of complex fluids: advantages and challenges. Zbl 1181.76019
Feng, James J.; Liu, Chun; Shen, Jie; Yue, Pengtao
2005
Decoupled energy stable schemes for a phase-field model of two-phase incompressible flows with variable density. Zbl 1326.76064
Liu, Chun; Shen, Jie; Yang, Xiaofeng
2015
Simulations of singularity dynamics in liquid crystal flows: a $$C^0$$ finite element approach. Zbl 1101.82039
Lin, Ping; Liu, Chun
2006
FENE dumbbell model and its several linear and nonlinear closure approximations. Zbl 1108.76006
Du, Qiang; Liu, Chun; Yu, Peng
2005
Modeling the spontaneous curvature effects in static cell membrane deformations by a phase field formulation. Zbl 1078.92004
Du, Q.; Liu, C.; Ryham, R.; Wang, X.
2005
Evolution of grain boundaries. Zbl 1036.74041
Kinderlehrer, David; Liu, Chun
2001
New Poisson-Boltzmann type equations: one-dimensional solutions. Zbl 1214.78012
Lee, Chiun-Chang; Lee, Hijin; Hyon, Yunkyong; Lin, Tai-Chia; Liu, Chun
2011
Mixed methods for the approximation of liquid crystal flows. Zbl 1032.76035
Liu, Chun; Walkington, Noel J.
2002
Finite time singularity of the nematic liquid crystal flow in dimension three. Zbl 1344.35104
Huang, Tao; Lin, Fanghua; Liu, Chun; Wang, Changyou
2016
Modeling and simulations of drop pinch-off from liquid crystal filaments and the leaky liquid crystal faucet immersed in viscous fluids. Zbl 1286.65112
Yang, Xiaofeng; Forest, M. Gregory; Li, Huiyuan; Liu, Chun; Shen, Jie; Wang, Qi; Chen, Falai
2013
Energy law preserving $$C^0$$ finite element schemes for phase field models in two-phase flow computations. Zbl 1408.76550
Hua, Jinsong; Lin, Ping; Liu, Chun; Wang, Qi
2011
Retrieving topological information for phase field models. Zbl 1114.74044
Du, Qiang; Liu, Chun; Wang, Xiaoqiang
2005
Mathematical models for the deformation of electrolyte droplets. Zbl 1147.35343
Ryham, Rolf; Liu, Chun; Zikatanov, Ludmil
2007
Existence and uniqueness of positive solutions for singular fractional differential systems with coupled integral boundary conditions. Zbl 1412.34099
Liu, Lishan; Li, Hongdan; Liu, Chun; Wu, Yonghong
2017
Convergence of numerical approximations of the incompressible Navier-Stokes equations with variable density and viscosity. Zbl 1138.76048
Liu, Chun; Walkington, Noel J.
2007
The phase transition between chiral nematic and smectic $$A^*$$ liquid crystals. Zbl 1032.76007
Bauman, Patricia; Calderer, M. Carme; Liu, Chun; Phillips, Daniel
2002
On liquid crystal flows with free-slip boundary conditions. Zbl 1014.76005
Liu, Chun; Shen, Jie
2001
An energetic variational approach for ion transport. Zbl 1319.35199
Xu, Shixin; Sheng, Ping; Liu, Chun
2014
Axisymmetric solutions to coupled Navier-Stokes/Allen-Cahn equations. Zbl 1203.35191
Xu, Xiang; Zhao, Liyun; Liu, Chun
2010
Energetic variational approaches for incompressible fluid systems on an evolving surface. Zbl 1358.37081
Koba, Hajime; Liu, Chun; Giga, Yoshikazu
2017
Asymptotic behavior for a nematic liquid crystal model with different kinematic transport properties. Zbl 1259.35040
Wu, Hao; Xu, Xiang; Liu, Chun
2012
Shear cell rupture of nematic liquid crystal droplets in viscous fluids. Zbl 1282.76061
Yang, Xiaofeng; Forest, M. Gregory; Liu, Chun; Shen, Jie
2011
Phase field model of thermo-induced Marangoni effects in the mixtures and its numerical simulations with mixed finite element method. Zbl 1364.76097
Sun, Pengtao; Liu, Chun; Xu, Jinchao
2009
Energy variational approach to study charge inversion (layering) near charged walls. Zbl 1257.82100
Hyon, Yunkyong; Fonseca, James E.; Eisenberg, Bob; Liu, Chun
2012
Dynamics of defect motion in nematic liquid crystal flow: modeling and numerical simulation. Zbl 1164.76422
Liu, Chun; Shen, Jie; Yang, Xiaofeng
2007
On electro-kinetic fluids: one-dimensional configurations. Zbl 1184.35262
Ryham, Rolf; Liu, Chun; Wang, Zhi-Qiang
2006
Dynamic theory for incompressible smectic-A liquid crystals: existence and regularity. Zbl 1021.35083
Liu, Chun
2000
Transient drop deformation upon startup of shear in viscoelastic fluids. Zbl 1188.76180
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
2005
From micro to macro dynamics via a new closure approximation to the FENE model of polymeric fluids. Zbl 1108.76007
Yu, Peng; Du, Qiang; Liu, Chun
2005
An energetic variational approach for the Cahn-Hilliard equation with dynamic boundary condition: model derivation and mathematical analysis. Zbl 1416.35209
Liu, Chun; Wu, Hao
2019
Diffusion limit of kinetic equations for multiple species charged particles. Zbl 1308.35311
Wu, Hao; Lin, Tai-Chia; Liu, Chun
2015
A model of electrodiffusion and osmotic water flow and its energetic structure. Zbl 1227.92007
Mori, Yoichiro; Liu, Chun; Eisenberg, Robert S.
2011
Time evolution of nematic liquid crystals with variable degree of orientation. Zbl 1003.35108
Calderer, M. C.; Golovaty, D.; Lin, F.-H.; Liu, C.
2002
Energetically stable discretizations for charge transport and electrokinetic models. Zbl 1351.78040
Metti, Maximilian S.; Xu, Jinchao; Liu, Chun
2016
Transport of charged particles: entropy production and maximum dissipation principle. Zbl 1345.76123
Hsieh, Chia-Yu; Hyon, YunKyong; Lee, Hijin; Lin, Tai-Chia; Liu, Chun
2015
Existence and stability for mathematical models of sedimentation-consolidation processes in several space dimensions. Zbl 0995.35050
Bürger, R.; Liu, C.; Wendland, W. L.
2001
High order finite difference and multigrid methods for spatially evolving instability in a planar channel. Zbl 0769.76038
Liu, C.; Liu, Z.
1993
Modeling and simulating asymmetrical conductance changes in gramicidin pores. Zbl 1323.92090
Xu, Shixin; Chen, Minxin; Majd, Sheereen; Yue, Xingye; Liu, Chun
2014
Non-isothermal general Ericksen-Leslie system: derivation, analysis and thermodynamic consistency. Zbl 1429.76032
De Anna, Francesco; Liu, Chun
2019
Boundary layer solutions of charge conserving Poisson-Boltzmann equations: one-dimensional case. Zbl 1344.76077
Lee, Chiun-Chang; Lee, Hijin; Hyon, Yunkyong; Lin, Tai-Chia; Liu, Chun
2016
Two-phase flow problem coupled with mean curvature flow. Zbl 1246.35212
Liu, Chun; Sato, Norifumi; Tonegawa, Yoshihiro
2012
Liquid crystal flow: Dynamic and static configurations. Zbl 0956.35104
Calderer, M. Carme; Liu, Chun
2000
Radial configurations of smectic A materials and focal conics. Zbl 0954.76004
Calderer, M. Carme; Liu, Chun; Voss, Karl
1998
Numerical simulations of hydrodynamics of nematic liquid crystals: effects of kinematic transports. Zbl 1364.76018
Zhang, Shupeng; Liu, Chun; Zhang, Hui
2011
On the existence of mean curvature flow with transport term. Zbl 1201.53076
Liu, Chun; Sato, Norifumi; Tonegawa, Yoshihiro
2010
Boundary conditions for the microscopic FENE models. Zbl 1147.76003
Liu, Chun; Liu, Hailiang
2008
A generalized Poisson-Nernst-Planck-Navier-Stokes model on the fluid with the crowded charged particles: derivation and its well-posedness. Zbl 1416.35220
Wang, Yong; Liu, Chun; Tan, Zhong
2016
Finite time singularities for hyperbolic systems. Zbl 1316.35005
Chen, Geng; Huang, Tao; Liu, Chun
2015
An enhanced macroscopic closure approximation to the micro-macro FENE model for polymeric materials. Zbl 1173.76001
Hyon, Yunkyong; Du, Qiang; Liu, Chun
2008
Diffuse interface energies capturing the Euler number: relaxation and renomalization. Zbl 1136.74007
Du, Qiang; Liu, Chun; Ryham, Rolf; Wang, Xiaoqiang
2007
Smectic A liquid crystal configurations with interface defects. Zbl 0988.76008
Calderer, M. Carme; Liu, Chun; Voss, Karl
2001
Numerical complete solution for random genetic drift by energetic variational approach. Zbl 1418.65150
Duan, Chenghua; Liu, Chun; Wang, Cheng; Yue, Xingye
2019
Non-isothermal electrokinetics: energetic variational approach. Zbl 1406.35290
Liu, Pei; Wu, Simo; Liu, Chun
2018
Inventory competition in a dual-channel supply chain with delivery lead time consideration. Zbl 1443.90081
Yang, J. Q.; Zhang, X. M.; Fu, H. Y.; Liu, C.
2017
Stability of a two-dimensional Poiseuille-type flow for a viscoelastic fluid. Zbl 1369.35057
Endo, Masakazu; Giga, Yoshikazu; Götz, Dario; Liu, Chun
2017
Diffuse interface methods for multiple phase materials: an energetic variational approach. Zbl 1349.76759
Brannick, J.; Liu, C.; Qian, T.; Sun, H.
2015
An improved interpolating element-free Galerkin method based on nonsingular weight functions. Zbl 1407.74091
Sun, F. X.; Liu, C.; Cheng, Y. M.
2014
First-order system least squares and the energetic variational approach for two-phase flow. Zbl 1408.76528
Adler, J. H.; Brannick, J.; Liu, C.; Manteuffel, T.; Zikatanov, L.
2011
Heart-shaped bubbles rising in anisotropic liquids. Zbl 1146.76583
Zhou, Chunfeng; Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
2007
On two nonlinear biharmonic evolution equations: existence, uniqueness and stability. Zbl 1071.35042
Lai, Ming-Jun; Liu, Chun; Wenston, Paul
2004
Bivariate spline method for numerical solution of time evolution Navier-Stokes equations over polygons in stream function formulation. Zbl 1075.76040
Lai, Ming-Jun; Liu, Chun; Wenston, Paul
2003
Existence of positive solutions for singular higher-order fractional differential equation via spectral analysis. Zbl 1377.34011
Guo, Limin; Liu, Chun
2017
Two-phase incompressible flows with variable density: an energetic variational approach. Zbl 1361.35129
Jiang, Jie; Li, Yinghua; Liu, Chun
2017
Strong solutions and instability for the fitness gradient system in evolutionary games between two populations. Zbl 1372.37137
Xu, Qiuju; Belmonte, Andrew; deForest, Russ; Liu, Chun; Tan, Zhong
2017
Well-posedness on a new hydrodynamic model of the fluid with the dilute charged particles. Zbl 1352.35127
Wang, Yong; Liu, Chun; Tan, Zhong
2017
Strong convergence of a general iterative algorithm for asymptotically nonexpansive semigroups in Banach spaces. Zbl 06807276
Liu, Lishan; Liu, Chun; Wang, Fang; Wu, Yonghong
2016
Blow-up criterion for compressible visco-elasticity equations in three dimensional space. Zbl 1301.35103
Du, Yi; Liu, Chun; Zhang, Qingtian
2014
Hydrodynamic boundary conditions for one-component liquid-gas flows on non-isothermal solid substrates. Zbl 1282.76179
Liu, Chun; Qian, Tiezheng; Xu, Xinpeng
2012
Onsager principle and electrorheological fluid dynamics. Zbl 1167.82018
Sheng, Ping; Zhang, Jianwei; Liu, Chun
2008
Numerical simulations on two nonlinear biharmonic evolution equations. Zbl 1051.65098
Lai, Ming-Jun; Liu, Chun; Wenston, Paul
2004
Mathematical developments in the study of smectic A liquid crystals. Zbl 1210.76024
Calderer, M. Carme; Liu, Chun
2000
Finite-element modelling of deformation and spread in slab rolling. Zbl 0604.73046
Liu, C.; Hartley, P.; Sturgess, C. E. N.; Rowe, G. W.
1987
A new Lagrange multiplier approach for gradient flows. Zbl 1442.65211
Cheng, Qing; Liu, Chun; Shen, Jie
2020
A new Lagrange multiplier approach for gradient flows. Zbl 1442.65211
Cheng, Qing; Liu, Chun; Shen, Jie
2020
An energetic variational approach for the Cahn-Hilliard equation with dynamic boundary condition: model derivation and mathematical analysis. Zbl 1416.35209
Liu, Chun; Wu, Hao
2019
Non-isothermal general Ericksen-Leslie system: derivation, analysis and thermodynamic consistency. Zbl 1429.76032
De Anna, Francesco; Liu, Chun
2019
Numerical complete solution for random genetic drift by energetic variational approach. Zbl 1418.65150
Duan, Chenghua; Liu, Chun; Wang, Cheng; Yue, Xingye
2019
Nonlinear simulation of an elastic tumor-host interface. Zbl 1425.92115
Lu, Min-Jhe; Liu, Chun; Li, Shuwang
2019
Non-isothermal electrokinetics: energetic variational approach. Zbl 1406.35290
Liu, Pei; Wu, Simo; Liu, Chun
2018
Integrated multiple-model adaptive fault identification and reconfigurable fault-tolerant control for lead-wing close formation systems. Zbl 1385.93041
Liu, Chun; Jiang, Bin; Zhang, Ke
2018
Existence of weak solutions to an evolutionary model for magnetoelasticity. Zbl 1390.74059
Benešová, Barbora; Forster, Johannes; Liu, Chun; Schlömerkemper, Anja
2018
Existence and uniqueness of positive solutions for singular fractional differential systems with coupled integral boundary conditions. Zbl 1412.34099
Liu, Lishan; Li, Hongdan; Liu, Chun; Wu, Yonghong
2017
Energetic variational approaches for incompressible fluid systems on an evolving surface. Zbl 1358.37081
Koba, Hajime; Liu, Chun; Giga, Yoshikazu
2017
Inventory competition in a dual-channel supply chain with delivery lead time consideration. Zbl 1443.90081
Yang, J. Q.; Zhang, X. M.; Fu, H. Y.; Liu, C.
2017
Stability of a two-dimensional Poiseuille-type flow for a viscoelastic fluid. Zbl 1369.35057
Endo, Masakazu; Giga, Yoshikazu; Götz, Dario; Liu, Chun
2017
Existence of positive solutions for singular higher-order fractional differential equation via spectral analysis. Zbl 1377.34011
Guo, Limin; Liu, Chun
2017
Two-phase incompressible flows with variable density: an energetic variational approach. Zbl 1361.35129
Jiang, Jie; Li, Yinghua; Liu, Chun
2017
Strong solutions and instability for the fitness gradient system in evolutionary games between two populations. Zbl 1372.37137
Xu, Qiuju; Belmonte, Andrew; deForest, Russ; Liu, Chun; Tan, Zhong
2017
Well-posedness on a new hydrodynamic model of the fluid with the dilute charged particles. Zbl 1352.35127
Wang, Yong; Liu, Chun; Tan, Zhong
2017
Largest well-posed spaces for the general diffusion system with nonlocal interactions. Zbl 1372.35309
Deng, Chao; Liu, Chun
2017
On partial regularity problem for 3D Boussinesq equations. Zbl 1372.35233
Fang, Daoyuan; Liu, Chun; Qian, Chenyin
2017
Finite time singularity of the nematic liquid crystal flow in dimension three. Zbl 1344.35104
Huang, Tao; Lin, Fanghua; Liu, Chun; Wang, Changyou
2016
Energetically stable discretizations for charge transport and electrokinetic models. Zbl 1351.78040
Metti, Maximilian S.; Xu, Jinchao; Liu, Chun
2016
Boundary layer solutions of charge conserving Poisson-Boltzmann equations: one-dimensional case. Zbl 1344.76077
Lee, Chiun-Chang; Lee, Hijin; Hyon, Yunkyong; Lin, Tai-Chia; Liu, Chun
2016
A generalized Poisson-Nernst-Planck-Navier-Stokes model on the fluid with the crowded charged particles: derivation and its well-posedness. Zbl 1416.35220
Wang, Yong; Liu, Chun; Tan, Zhong
2016
Strong convergence of a general iterative algorithm for asymptotically nonexpansive semigroups in Banach spaces. Zbl 06807276
Liu, Lishan; Liu, Chun; Wang, Fang; Wu, Yonghong
2016
Decoupled energy stable schemes for a phase-field model of two-phase incompressible flows with variable density. Zbl 1326.76064
Liu, Chun; Shen, Jie; Yang, Xiaofeng
2015
Diffusion limit of kinetic equations for multiple species charged particles. Zbl 1308.35311
Wu, Hao; Lin, Tai-Chia; Liu, Chun
2015
Transport of charged particles: entropy production and maximum dissipation principle. Zbl 1345.76123
Hsieh, Chia-Yu; Hyon, YunKyong; Lee, Hijin; Lin, Tai-Chia; Liu, Chun
2015
Finite time singularities for hyperbolic systems. Zbl 1316.35005
Chen, Geng; Huang, Tao; Liu, Chun
2015
Diffuse interface methods for multiple phase materials: an energetic variational approach. Zbl 1349.76759
Brannick, J.; Liu, C.; Qian, T.; Sun, H.
2015
An energetic variational approach for ion transport. Zbl 1319.35199
Xu, Shixin; Sheng, Ping; Liu, Chun
2014
Modeling and simulating asymmetrical conductance changes in gramicidin pores. Zbl 1323.92090
Xu, Shixin; Chen, Minxin; Majd, Sheereen; Yue, Xingye; Liu, Chun
2014
An improved interpolating element-free Galerkin method based on nonsingular weight functions. Zbl 1407.74091
Sun, F. X.; Liu, C.; Cheng, Y. M.
2014
Blow-up criterion for compressible visco-elasticity equations in three dimensional space. Zbl 1301.35103
Du, Yi; Liu, Chun; Zhang, Qingtian
2014
An energetic variational approach to ion channel dynamics. Zbl 1302.35375
Hyon, YunKyong; Eisenberg, Bob; Liu, Chun
2014
On the general Ericksen-Leslie system: Parodi’s relation, well-posedness and stability. Zbl 1320.76010
Wu, Hao; Xu, Xiang; Liu, Chun
2013
Modeling and simulations of drop pinch-off from liquid crystal filaments and the leaky liquid crystal faucet immersed in viscous fluids. Zbl 1286.65112
Yang, Xiaofeng; Forest, M. Gregory; Li, Huiyuan; Liu, Chun; Shen, Jie; Wang, Qi; Chen, Falai
2013
High-order mixed weighted compact and non-compact scheme for shock and small length scale interaction. Zbl 1278.76049
Stipcich, G.; Fu, H.; Liu, C.
2013
$$\theta_{13}$$ and the Higgs mass from high scale supersymmetry. Zbl 1264.81319
Liu, Chun; Zhao, Zhen-Hua
2013
Asymptotic behavior for a nematic liquid crystal model with different kinematic transport properties. Zbl 1259.35040
Wu, Hao; Xu, Xiang; Liu, Chun
2012
Energy variational approach to study charge inversion (layering) near charged walls. Zbl 1257.82100
Hyon, Yunkyong; Fonseca, James E.; Eisenberg, Bob; Liu, Chun
2012
Two-phase flow problem coupled with mean curvature flow. Zbl 1246.35212
Liu, Chun; Sato, Norifumi; Tonegawa, Yoshihiro
2012
Hydrodynamic boundary conditions for one-component liquid-gas flows on non-isothermal solid substrates. Zbl 1282.76179
Liu, Chun; Qian, Tiezheng; Xu, Xinpeng
2012
A mathematical model for the hard sphere repulsion in ionic solutions. Zbl 1406.76089
Hyon, Yunkyong; Eisenberg, Bob; Liu, Chun
2011
New Poisson-Boltzmann type equations: one-dimensional solutions. Zbl 1214.78012
Lee, Chiun-Chang; Lee, Hijin; Hyon, Yunkyong; Lin, Tai-Chia; Liu, Chun
2011
Energy law preserving $$C^0$$ finite element schemes for phase field models in two-phase flow computations. Zbl 1408.76550
Hua, Jinsong; Lin, Ping; Liu, Chun; Wang, Qi
2011
Shear cell rupture of nematic liquid crystal droplets in viscous fluids. Zbl 1282.76061
Yang, Xiaofeng; Forest, M. Gregory; Liu, Chun; Shen, Jie
2011
A model of electrodiffusion and osmotic water flow and its energetic structure. Zbl 1227.92007
Mori, Yoichiro; Liu, Chun; Eisenberg, Robert S.
2011
Numerical simulations of hydrodynamics of nematic liquid crystals: effects of kinematic transports. Zbl 1364.76018
Zhang, Shupeng; Liu, Chun; Zhang, Hui
2011
First-order system least squares and the energetic variational approach for two-phase flow. Zbl 1408.76528
Adler, J. H.; Brannick, J.; Liu, C.; Manteuffel, T.; Zikatanov, L.
2011
Energetic variational approach in complex fluids: maximum dissipation principle. Zbl 1423.76380
Hyon, Yunkyong; Kwak, Do Young; Liu, Chun
2010
Axisymmetric solutions to coupled Navier-Stokes/Allen-Cahn equations. Zbl 1203.35191
Xu, Xiang; Zhao, Liyun; Liu, Chun
2010
On the existence of mean curvature flow with transport term. Zbl 1201.53076
Liu, Chun; Sato, Norifumi; Tonegawa, Yoshihiro
2010
On energetic variational approaches in modeling the nematic liquid crystal flows. Zbl 1156.76007
Sun, Huan; Liu, Chun
2009
Energetic variational approaches in modeling vesicle and fluid interactions. Zbl 1183.74056
Du, Qiang; Liu, Chun; Ryham, Rolf; Wang, Xiaoqiang
2009
Phase field model of thermo-induced Marangoni effects in the mixtures and its numerical simulations with mixed finite element method. Zbl 1364.76097
Sun, Pengtao; Liu, Chun; Xu, Jinchao
2009
Global solutions for incompressible viscoelastic fluids. Zbl 1138.76017
Lei, Zhen; Liu, Chun; Zhou, Yi
2008
Boundary conditions for the microscopic FENE models. Zbl 1147.76003
Liu, Chun; Liu, Hailiang
2008
An enhanced macroscopic closure approximation to the micro-macro FENE model for polymeric materials. Zbl 1173.76001
Hyon, Yunkyong; Du, Qiang; Liu, Chun
2008
Onsager principle and electrorheological fluid dynamics. Zbl 1167.82018
Sheng, Ping; Zhang, Jianwei; Liu, Chun
2008
The nucleation and growth of gas bubbles in a Newtonian fluid: an energetic variational phase field approach. Zbl 1306.76050
Naber, Aaron; Liu, Chun; Feng, James J.
2008
Analysis of a phase field Navier-Stokes vesicle-fluid interaction model. Zbl 1172.74016
Du, Qiang; Li, Manlin; Liu, Chun
2007
Global existence for a 2D incompressible viscoelastic model with small strain. Zbl 1132.76008
Lei, Zhen; Liu, Chun; Zhou, Yi
2007
Analysis of finite element approximations of a phase field model for two-phase fluids. Zbl 1111.76028
Feng, Xiaobing; He, Yinnian; Liu, Chun
2007
An energy law preserving $$C^0$$ finite element scheme for simulating the kinematic effects in liquid crystal dynamics. Zbl 1133.65077
Lin, Ping; Liu, Chun; Zhang, Hui
2007
On a micro-macro model for polymeric fluids near equilibrium. Zbl 1113.76017
Lin, Fang-Hua; Liu, Chun; Zhang, Ping
2007
Mathematical models for the deformation of electrolyte droplets. Zbl 1147.35343
Ryham, Rolf; Liu, Chun; Zikatanov, Ludmil
2007
Convergence of numerical approximations of the incompressible Navier-Stokes equations with variable density and viscosity. Zbl 1138.76048
Liu, Chun; Walkington, Noel J.
2007
Dynamics of defect motion in nematic liquid crystal flow: modeling and numerical simulation. Zbl 1164.76422
Liu, Chun; Shen, Jie; Yang, Xiaofeng
2007
Diffuse interface energies capturing the Euler number: relaxation and renomalization. Zbl 1136.74007
Du, Qiang; Liu, Chun; Ryham, Rolf; Wang, Xiaoqiang
2007
Heart-shaped bubbles rising in anisotropic liquids. Zbl 1146.76583
Zhou, Chunfeng; Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
2007
Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method. Zbl 1158.76319
Yang, Xiaofeng; Feng, James J.; Liu, Chun; Shen, Jie
2006
Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions. Zbl 1086.74024
Du, Qiang; Liu, Chun; Wang, Xiaoqiang
2006
Simulations of singularity dynamics in liquid crystal flows: a $$C^0$$ finite element approach. Zbl 1101.82039
Lin, Ping; Liu, Chun
2006
On electro-kinetic fluids: one-dimensional configurations. Zbl 1184.35262
Ryham, Rolf; Liu, Chun; Wang, Zhi-Qiang
2006
A model for total energy of nematic elastomers with non-uniform prolate spheroids. Zbl 1118.82015
Calderer, Maria-Carme; Liu, Chun; Yan, Baisheng
2006
On hydrodynamics of viscoelastic fluids. Zbl 1076.76006
Lin, Fang-Hua; Liu, Chun; Zhang, Ping
2005
A phase field formulation of the Willmore problem. Zbl 1125.35366
Du, Qiang; Liu, Chun; Ryham, Rolf; Wang, Xiaoqiang
2005
Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids. Zbl 1195.76120
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
2005
Viscoelastic effects on drop deformation in steady shear. Zbl 1082.76007
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
2005
An energetic variational formulation with phase field methods for interfacial dynamics of complex fluids: advantages and challenges. Zbl 1181.76019
Feng, James J.; Liu, Chun; Shen, Jie; Yue, Pengtao
2005
FENE dumbbell model and its several linear and nonlinear closure approximations. Zbl 1108.76006
Du, Qiang; Liu, Chun; Yu, Peng
2005
Modeling the spontaneous curvature effects in static cell membrane deformations by a phase field formulation. Zbl 1078.92004
Du, Q.; Liu, C.; Ryham, R.; Wang, X.
2005
Retrieving topological information for phase field models. Zbl 1114.74044
Du, Qiang; Liu, Chun; Wang, Xiaoqiang
2005
Transient drop deformation upon startup of shear in viscoelastic fluids. Zbl 1188.76180
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
2005
From micro to macro dynamics via a new closure approximation to the FENE model of polymeric fluids. Zbl 1108.76007
Yu, Peng; Du, Qiang; Liu, Chun
2005
Dynamic steady-state stress field in a web during slitting. Zbl 1111.74522
Liu, C.; Lu, Hongbin; Huang, Young
2005
A diffuse-interface method for simulating two-phase flows of complex fluids. Zbl 1130.76437
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
2004
A phase field approach in the numerical study of the elastic bending energy for vesicle membranes. Zbl 1116.74384
Du, Qiang; Liu, Chun; Wang, Xiaoqiang
2004
On two nonlinear biharmonic evolution equations: existence, uniqueness and stability. Zbl 1071.35042
Lai, Ming-Jun; Liu, Chun; Wenston, Paul
2004
Numerical simulations on two nonlinear biharmonic evolution equations. Zbl 1051.65098
Lai, Ming-Jun; Liu, Chun; Wenston, Paul
2004
A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method. Zbl 1092.76069
Liu, Chun; Shen, Jie
2003
Bivariate spline method for numerical solution of time evolution Navier-Stokes equations over polygons in stream function formulation. Zbl 1075.76040
Lai, Ming-Jun; Liu, Chun; Wenston, Paul
2003
Mixed methods for the approximation of liquid crystal flows. Zbl 1032.76035
Liu, Chun; Walkington, Noel J.
2002
The phase transition between chiral nematic and smectic $$A^*$$ liquid crystals. Zbl 1032.76007
Bauman, Patricia; Calderer, M. Carme; Liu, Chun; Phillips, Daniel
2002
Time evolution of nematic liquid crystals with variable degree of orientation. Zbl 1003.35108
Calderer, M. C.; Golovaty, D.; Lin, F.-H.; Liu, C.
2002
Hierarchical shape modeling for automatic face localization. Zbl 1039.68675
Liu, C.; Shum, H.-Y.; Zhang, C.
2002
Axisymmetric configurations of bipolar liquid crystal droplets. Zbl 1023.76006
Shen, Quan; Liu, Chun; Calderer, M. Carme
2002
An Eulerian description of fluids containing viscoelastic particles. Zbl 1009.76093
Liu, Chun; Walkington, Noel J.
2001
Static and dynamic theories of liquid crystals. Zbl 1433.82014
Lin, Fanghua; Liu, Chun
2001
Evolution of grain boundaries. Zbl 1036.74041
Kinderlehrer, David; Liu, Chun
2001
On liquid crystal flows with free-slip boundary conditions. Zbl 1014.76005
Liu, Chun; Shen, Jie
2001
...and 14 more Documents
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#### Cited by 1,846 Authors

 47 Liu, Chun 35 Yang, Xiaofeng 31 Liu, Qiao 27 Shen, Jie 20 Guillén González, Francisco M. 20 Wang, Qi 17 Zhao, Jia 16 Fan, Jishan 15 Hu, Xianpeng 15 Kim, Junseok 15 Lowengrub, John Samuel 15 Wang, Changyou 15 Wang, Dehua 15 Zhao, Jihong 14 Yao, Zhengan 13 Wu, Hao 13 Zhang, Zhifei 12 Du, Qiang 12 Lin, Fang Hua 11 Feng, James J. 11 Rocca, Elisabetta 11 Yue, Pengtao 11 Zarnescu, Arghir Dani 10 Jiang, Fei 10 Lei, Zhen 10 Nochetto, Ricardo Horacio 10 Shu, Chang 10 Tan, Zhong 10 Voigt, Axel 10 Wang, Xiaoqiang 10 Xu, Xiang 9 Ding, Shijin 9 Grasselli, Maurizio 9 Lin, Ping 9 Liu, Weishi 9 Schimperna, Giulio 9 Wang, Wei 9 Xu, Jinchao 9 Zi, Ruizhao 8 Abels, Helmut 8 Barrett, John W. 8 Gal, Ciprian Gheorghe Sorin 8 Han, Daozhi 8 Hieber, Matthias 8 Huang, Jinrui 8 Lee, Hyun Geun 8 Liu, Lishan 8 Walker, Shawn W. 8 Wang, Cheng 8 Yuan, Baoquan 8 Zhang, Pingwen 7 Ding, Hang 7 Gong, Yuezheng 7 Guo, Boling 7 He, Xiaoming 7 Huang, Tao 7 Li, Jinkai 7 Liu, Shengquan 7 Masmoudi, Nader 7 Miranville, Alain M. 7 Mori, Yoichiro 7 Sarkar, Kausik 7 Süli, Endre E. 7 Tonegawa, Yoshihiro 7 Wen, Huanyao 7 Wise, Steven M. 7 Yu, Haijun 7 Zhang, Mingji 7 Zhang, Ping 7 Zhang, Ting 7 Zhou, Yong 6 Adler, James H. 6 Afkhami, Shahriar 6 Calderer, Maria-Carme T. 6 Climent-Ezquerra, Blanca 6 Fang, Daoyuan 6 Garcke, Harald 6 Ju, Lili 6 Lee, Chiun-Chang 6 Li, Shuwang 6 Li, Xiaoli 6 Li, Yin 6 Lin, Junyu 6 Liu, Xiangao 6 Ratiu, Tudor Stefan 6 Soldati, Alfredo 6 Tachim Medjo, Theodore 6 Tierra, Giordano 6 Wei, Ruiying 6 Wu, Yonghong 5 Anderson, Patrick D. 5 Bie, Qunyi 5 Chechkin, Gregory A. 5 Constantin, Peter 5 De Anna, Francesco 5 Gala, Sadek 5 Hong, Minchun 5 Hsieh, Chia-Yu 5 Hulsen, Martien A. 5 Khoo, Boo Cheong ...and 1,746 more Authors
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#### Cited in 184 Serials

 177 Journal of Computational Physics 63 Journal of Differential Equations 54 Archive for Rational Mechanics and Analysis 43 Computers and Fluids 42 Journal of Scientific Computing 38 Computer Methods in Applied Mechanics and Engineering 36 Journal of Fluid Mechanics 35 Journal of Mathematical Analysis and Applications 30 Computers & Mathematics with Applications 30 Mathematical Methods in the Applied Sciences 28 SIAM Journal on Mathematical Analysis 24 Discrete and Continuous Dynamical Systems 22 Journal of Computational and Applied Mathematics 22 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 22 SIAM Journal on Scientific Computing 22 Journal of Mathematical Fluid Mechanics 21 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 17 ZAMP. Zeitschrift für angewandte Mathematik und Physik 17 SIAM Journal on Applied Mathematics 17 Communications on Pure and Applied Analysis 16 Physica D 16 Calculus of Variations and Partial Differential Equations 14 Applied Mathematics and Computation 14 Nonlinear Analysis. Real World Applications 13 Journal of Functional Analysis 12 Mathematics of Computation 11 International Journal for Numerical Methods in Fluids 11 Journal of Mathematical Physics 11 Numerische Mathematik 11 Applied Mathematics Letters 11 Discrete and Continuous Dynamical Systems. Series B 11 Journal of Theoretical Biology 10 Communications in Mathematical Physics 9 Applicable Analysis 9 Communications on Pure and Applied Mathematics 9 Acta Applicandae Mathematicae 9 Applied Numerical Mathematics 9 Journal of Non-Newtonian Fluid Mechanics 9 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 8 SIAM Journal on Numerical Analysis 8 Chinese Annals of Mathematics. Series B 8 Applied Mathematical Modelling 8 Physics of Fluids 7 International Journal for Numerical Methods in Engineering 7 Boundary Value Problems 6 Bulletin of Mathematical Biology 6 Mathematische Annalen 6 Quarterly of Applied Mathematics 6 Communications in Partial Differential Equations 6 European Journal of Mechanics. B. Fluids 6 Molecular Based Mathematical Biology 6 Journal of Function Spaces 5 Journal of Mathematical Biology 5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 Journal of Nonlinear Science 5 Abstract and Applied Analysis 5 Journal of Evolution Equations 5 Discrete and Continuous Dynamical Systems. Series S 5 Science China. Mathematics 4 Journal of Statistical Physics 4 Advances in Mathematics 4 European Journal of Applied Mathematics 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Journal of Dynamics and Differential Equations 4 NoDEA. Nonlinear Differential Equations and Applications 4 Advances in Computational Mathematics 4 Engineering Analysis with Boundary Elements 4 International Journal of Computational Methods 4 Computational and Mathematical Biophysics 3 Computer Physics Communications 3 International Journal of Engineering Science 3 Nonlinearity 3 Physica A 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Mathematische Nachrichten 3 Computational Mechanics 3 Mathematical Problems in Engineering 3 Mathematical Physics, Analysis and Geometry 3 Acta Mathematica Sinica. English Series 3 Communications in Nonlinear Science and Numerical Simulation 3 Nonlinear Analysis. Modelling and Control 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Analysis and Applications (Singapore) 3 Frontiers of Mathematics in China 3 Kinetic and Related Models 2 Acta Mechanica 2 Mathematical Biosciences 2 Annales Polonici Mathematici 2 Calcolo 2 Meccanica 2 Transactions of the American Mathematical Society 2 Numerical Methods for Partial Differential Equations 2 Mathematical and Computer Modelling 2 Journal of Mathematical Imaging and Vision 2 Potential Analysis 2 Applicationes Mathematicae 2 Computational and Applied Mathematics 2 International Journal of Numerical Methods for Heat & Fluid Flow 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Interfaces and Free Boundaries ...and 84 more Serials
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#### Cited in 39 Fields

 925 Fluid mechanics (76-XX) 723 Partial differential equations (35-XX) 372 Numerical analysis (65-XX) 158 Statistical mechanics, structure of matter (82-XX) 134 Mechanics of deformable solids (74-XX) 107 Biology and other natural sciences (92-XX) 45 Calculus of variations and optimal control; optimization (49-XX) 34 Classical thermodynamics, heat transfer (80-XX) 33 Differential geometry (53-XX) 31 Ordinary differential equations (34-XX) 23 Dynamical systems and ergodic theory (37-XX) 23 Optics, electromagnetic theory (78-XX) 17 Probability theory and stochastic processes (60-XX) 13 Global analysis, analysis on manifolds (58-XX) 12 Operator theory (47-XX) 8 Real functions (26-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 5 Integral equations (45-XX) 5 Geophysics (86-XX) 5 Operations research, mathematical programming (90-XX) 5 Systems theory; control (93-XX) 4 General and overarching topics; collections (00-XX) 4 Computer science (68-XX) 3 Combinatorics (05-XX) 3 Functional analysis (46-XX) 3 Mechanics of particles and systems (70-XX) 3 Quantum theory (81-XX) 3 Information and communication theory, circuits (94-XX) 2 Measure and integration (28-XX) 2 Functions of a complex variable (30-XX) 2 Approximations and expansions (41-XX) 2 Statistics (62-XX) 2 Astronomy and astrophysics (85-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Algebraic geometry (14-XX) 1 Special functions (33-XX) 1 Integral transforms, operational calculus (44-XX) 1 Algebraic topology (55-XX) 1 Relativity and gravitational theory (83-XX)