# zbMATH — the first resource for mathematics

## Cao, Chongsheng

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 Author ID: cao.chongsheng Published as: Cao, C.; Cao, Chongsheng
 Documents Indexed: 36 Publications since 1999
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#### Co-Authors

 1 single-authored 22 Titi, Edriss Saleh 10 Wu, Jiahong 4 Adhikari, Dhanapati 4 Li, Jinkai 2 Farhat, Aseel 2 Guo, Yanqiu 2 Rammaha, Mohammad A. 2 Xu, Xiaojing 1 Gal, Ciprian Gheorghe Sorin 1 Holm, Darryl D. 1 Ibrahim, Slim 1 Kevrekidis, Ioannis George 1 Lin, Quyuan 1 Nakanishi, Kenji 1 Qin, Junlin 1 Regmi, Dipendra 1 Shang, Haifeng 1 Ye, Zhuan 1 Yuan, Baoquan 1 Ziane, Mohammed
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#### Serials

 8 Journal of Differential Equations 3 Archive for Rational Mechanics and Analysis 3 Communications in Mathematical Physics 2 Communications on Pure and Applied Mathematics 2 Nonlinearity 2 Indiana University Mathematics Journal 2 Journal of Dynamics and Differential Equations 1 Journal of Mathematical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Advances in Mathematics 1 Journal of Functional Analysis 1 Communications in Partial Differential Equations 1 SIAM Journal on Mathematical Analysis 1 Discrete and Continuous Dynamical Systems 1 Journal of Mathematical Fluid Mechanics 1 Annals of Mathematics. Second Series 1 Communications in Information and Systems
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#### Fields

 34 Partial differential equations (35-XX) 28 Fluid mechanics (76-XX) 12 Geophysics (86-XX) 5 Dynamical systems and ergodic theory (37-XX) 1 Numerical analysis (65-XX) 1 Mechanics of deformable solids (74-XX) 1 Astronomy and astrophysics (85-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH

32 Publications have been cited 1,425 times in 790 Documents Cited by Year
Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion. Zbl 1213.35159
Cao, Chongsheng; Wu, Jiahong
2011
Two regularity criteria for the 3D MHD equations. Zbl 1190.35046
Cao, Chongsheng; Wu, Jiahong
2010
Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics. Zbl 1151.35074
Cao, Chongsheng; Titi, Edriss S.
2007
Regularity criteria for the three-dimensional Navier-Stokes equations. Zbl 1159.35053
Cao, Chongsheng; Titi, Edriss S.
2008
Global regularity for the two-dimensional anisotropic Boussinesq equations with vertical dissipation. Zbl 1284.35140
Cao, Chongsheng; Wu, Jiahong
2013
Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor. Zbl 1256.35051
Cao, Chongsheng; Titi, Edriss S.
2011
The 2D incompressible magnetohydrodynamics equations with only magnetic diffusion. Zbl 1293.35233
Cao, Chongsheng; Wu, Jiahong; Yuan, Baoquan
2014
The 2D MHD equations with horizontal dissipation and horizontal magnetic diffusion. Zbl 1270.35143
Cao, Chongsheng; Regmi, Dipendra; Wu, Jiahong
2013
Global regularity results for the 2D Boussinesq equations with vertical dissipation. Zbl 1232.35111
Adhikari, Dhanapati; Cao, Chongsheng; Wu, Jiahong
2011
Traveling wave solutions for a class of one-dimensional nonlinear shallow water wave models. Zbl 1062.35080
Cao, Chongsheng; Holm, Darryl D.; Titi, Edriss S.
2004
Global well-posedness and finite-dimensional global attractor for a 3-D planetary geostrophic viscous model. Zbl 1035.37043
Cao, Chongsheng; Titi, Edriss S.
2003
The 2D Boussinesq equations with vertical viscosity and vertical diffusivity. Zbl 1193.35144
Adhikari, Dhanapati; Cao, Chongsheng; Wu, Jiahong
2010
The Navier-Stokes equations on the rotating 2-D sphere: Gevrey regularity and asymptotic degrees of freedom. Zbl 0928.35120
Cao, Chongsheng; Rammaha, Mohammad A.; Titi, Edriss S.
1999
Sufficient conditions for the regularity to the 3D Navier-Stokes equations. Zbl 1186.35136
Cao, Chongsheng
2010
Global regularity results for the 2D Boussinesq equations with partial dissipation. Zbl 1328.35161
Adhikari, Dhanapati; Cao, Chongsheng; Shang, Haifeng; Wu, Jiahong; Xu, Xiaojing; Ye, Zhuan
2016
Finite-time blowup for the inviscid primitive equations of oceanic and atmospheric dynamics. Zbl 1317.35262
Cao, Chongsheng; Ibrahim, Slim; Nakanishi, Kenji; Titi, Edriss S.
2015
Global solutions for the 2D NS-CH model for a two-phase flow of viscous, incompressible fluids with mixed partial viscosity and mobility. Zbl 1259.35048
Cao, Chongsheng; Gal, Ciprian G.
2012
Local and global well-posedness of strong solutions to the 3D primitive equations with vertical Eddy diffusivity. Zbl 1305.35113
Cao, Chongsheng; Li, Jinkai; Titi, Edriss S.
2014
Global well-posedness of the $$3D$$ primitive equations with partial vertical turbulence mixing heat diffusion. Zbl 1267.35157
Cao, Chongsheng; Titi, Edriss S.
2012
Global well-posedness of strong solutions to the 3D primitive equations with horizontal eddy diffusivity. Zbl 1300.35089
Cao, Chongsheng; Li, Jinkai; Titi, Edriss S.
2014
Small global solutions to the damped two-dimensional Boussinesq equations. Zbl 1290.35193
Adhikari, Dhanapati; Cao, Chongsheng; Wu, Jiahong; Xu, Xiaojing
2014
Global well-posedness of the three-dimensional primitive equations with only horizontal viscosity and diffusion. Zbl 1351.35125
Cao, Chongsheng; Li, Jinkai; Titi, Edriss S.
2016
Gevrey regularity for nonlinear analytic parabolic equations on the sphere. Zbl 0967.35063
Cao, Chongsheng; Rammaha, Mohammad A.; Titi, Edriss S.
2000
Strong solutions to the 3D primitive equations with only horizontal dissipation: near $$H^{1}$$ initial data. Zbl 1366.35123
Cao, Chongsheng; Li, Jinkai; Titi, Edriss S.
2017
Regularity criterion for solutions of three-dimensional turbulent channel flows. Zbl 1151.76012
Cao, Chongsheng; Qin, Junlin; Titi, Edriss S.
2008
A ‘horizontal’ hyper-diffusion three-dimensonal thermocline planetary geostrophic model: well-posedness and long-time behaviour. Zbl 1070.35028
Cao, Chongsheng; Titi, Edriss S.; Ziane, Mohammed
2004
Numerical criterion for the stabilization of steady states of the Navier-Stokes equations. Zbl 0997.35048
Cao, Chongsheng; Kevrekidis, Ioannis G.; Titi, Edriss S.
2001
A new hybrid finite element approach for three-dimensional elastic problems. Zbl 1291.74175
Cao, C.; Qin, Q.-H.; Yu, A.
2012
Global well-posedness of an inviscid three-dimensional pseudo-Hasegawa-Mima model. Zbl 1308.35200
Cao, Chongsheng; Farhat, Aseel; Titi, Edriss S.
2013
Asymptotic behavior of viscous 1-D scalar conservation laws with Neumann boundary conditions. Zbl 1026.35068
Cao, Chongsheng; Titi, Edriss S.
2002
Global regularity theory for the incompressible magnetohydrodynamic type equations. Zbl 1296.35138
Cao, Chongsheng; Wu, Jiahong
2012
Global strong solutions for the three-dimensional Hasegawa-Mima model with partial dissipation. Zbl 1394.76053
Cao, Chongsheng; Guo, Yanqiu; Titi, Edriss S.
2018
Global strong solutions for the three-dimensional Hasegawa-Mima model with partial dissipation. Zbl 1394.76053
Cao, Chongsheng; Guo, Yanqiu; Titi, Edriss S.
2018
Strong solutions to the 3D primitive equations with only horizontal dissipation: near $$H^{1}$$ initial data. Zbl 1366.35123
Cao, Chongsheng; Li, Jinkai; Titi, Edriss S.
2017
Global regularity results for the 2D Boussinesq equations with partial dissipation. Zbl 1328.35161
Adhikari, Dhanapati; Cao, Chongsheng; Shang, Haifeng; Wu, Jiahong; Xu, Xiaojing; Ye, Zhuan
2016
Global well-posedness of the three-dimensional primitive equations with only horizontal viscosity and diffusion. Zbl 1351.35125
Cao, Chongsheng; Li, Jinkai; Titi, Edriss S.
2016
Finite-time blowup for the inviscid primitive equations of oceanic and atmospheric dynamics. Zbl 1317.35262
Cao, Chongsheng; Ibrahim, Slim; Nakanishi, Kenji; Titi, Edriss S.
2015
The 2D incompressible magnetohydrodynamics equations with only magnetic diffusion. Zbl 1293.35233
Cao, Chongsheng; Wu, Jiahong; Yuan, Baoquan
2014
Local and global well-posedness of strong solutions to the 3D primitive equations with vertical Eddy diffusivity. Zbl 1305.35113
Cao, Chongsheng; Li, Jinkai; Titi, Edriss S.
2014
Global well-posedness of strong solutions to the 3D primitive equations with horizontal eddy diffusivity. Zbl 1300.35089
Cao, Chongsheng; Li, Jinkai; Titi, Edriss S.
2014
Small global solutions to the damped two-dimensional Boussinesq equations. Zbl 1290.35193
Adhikari, Dhanapati; Cao, Chongsheng; Wu, Jiahong; Xu, Xiaojing
2014
Global regularity for the two-dimensional anisotropic Boussinesq equations with vertical dissipation. Zbl 1284.35140
Cao, Chongsheng; Wu, Jiahong
2013
The 2D MHD equations with horizontal dissipation and horizontal magnetic diffusion. Zbl 1270.35143
Cao, Chongsheng; Regmi, Dipendra; Wu, Jiahong
2013
Global well-posedness of an inviscid three-dimensional pseudo-Hasegawa-Mima model. Zbl 1308.35200
Cao, Chongsheng; Farhat, Aseel; Titi, Edriss S.
2013
Global solutions for the 2D NS-CH model for a two-phase flow of viscous, incompressible fluids with mixed partial viscosity and mobility. Zbl 1259.35048
Cao, Chongsheng; Gal, Ciprian G.
2012
Global well-posedness of the $$3D$$ primitive equations with partial vertical turbulence mixing heat diffusion. Zbl 1267.35157
Cao, Chongsheng; Titi, Edriss S.
2012
A new hybrid finite element approach for three-dimensional elastic problems. Zbl 1291.74175
Cao, C.; Qin, Q.-H.; Yu, A.
2012
Global regularity theory for the incompressible magnetohydrodynamic type equations. Zbl 1296.35138
Cao, Chongsheng; Wu, Jiahong
2012
Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion. Zbl 1213.35159
Cao, Chongsheng; Wu, Jiahong
2011
Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor. Zbl 1256.35051
Cao, Chongsheng; Titi, Edriss S.
2011
Global regularity results for the 2D Boussinesq equations with vertical dissipation. Zbl 1232.35111
Adhikari, Dhanapati; Cao, Chongsheng; Wu, Jiahong
2011
Two regularity criteria for the 3D MHD equations. Zbl 1190.35046
Cao, Chongsheng; Wu, Jiahong
2010
The 2D Boussinesq equations with vertical viscosity and vertical diffusivity. Zbl 1193.35144
Adhikari, Dhanapati; Cao, Chongsheng; Wu, Jiahong
2010
Sufficient conditions for the regularity to the 3D Navier-Stokes equations. Zbl 1186.35136
Cao, Chongsheng
2010
Regularity criteria for the three-dimensional Navier-Stokes equations. Zbl 1159.35053
Cao, Chongsheng; Titi, Edriss S.
2008
Regularity criterion for solutions of three-dimensional turbulent channel flows. Zbl 1151.76012
Cao, Chongsheng; Qin, Junlin; Titi, Edriss S.
2008
Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics. Zbl 1151.35074
Cao, Chongsheng; Titi, Edriss S.
2007
Traveling wave solutions for a class of one-dimensional nonlinear shallow water wave models. Zbl 1062.35080
Cao, Chongsheng; Holm, Darryl D.; Titi, Edriss S.
2004
A ‘horizontal’ hyper-diffusion three-dimensonal thermocline planetary geostrophic model: well-posedness and long-time behaviour. Zbl 1070.35028
Cao, Chongsheng; Titi, Edriss S.; Ziane, Mohammed
2004
Global well-posedness and finite-dimensional global attractor for a 3-D planetary geostrophic viscous model. Zbl 1035.37043
Cao, Chongsheng; Titi, Edriss S.
2003
Asymptotic behavior of viscous 1-D scalar conservation laws with Neumann boundary conditions. Zbl 1026.35068
Cao, Chongsheng; Titi, Edriss S.
2002
Numerical criterion for the stabilization of steady states of the Navier-Stokes equations. Zbl 0997.35048
Cao, Chongsheng; Kevrekidis, Ioannis G.; Titi, Edriss S.
2001
Gevrey regularity for nonlinear analytic parabolic equations on the sphere. Zbl 0967.35063
Cao, Chongsheng; Rammaha, Mohammad A.; Titi, Edriss S.
2000
The Navier-Stokes equations on the rotating 2-D sphere: Gevrey regularity and asymptotic degrees of freedom. Zbl 0928.35120
Cao, Chongsheng; Rammaha, Mohammad A.; Titi, Edriss S.
1999
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#### Cited by 741 Authors

 36 Wu, Jiahong 33 Titi, Edriss Saleh 29 Ye, Zhuan 28 Tachim Medjo, Theodore 25 Zhang, Zujin 23 Yamazaki, Kazuo 19 Xu, Xiaojing 18 Cao, Chongsheng 17 Temam, Roger Meyer 15 Gala, Sadek 14 Liu, Qiao 14 Nguyen Huy Tuan 13 Himonas, A. Alexandrou 13 Ragusa, Maria Alessandra 12 Skalák, Zdeněk 12 Zhou, Yong 11 Guo, Zhengguang 11 Liu, Yue 11 You, Bo 11 Yuan, Baoquan 11 Zhai, Xiaoping 10 He, Yinnian 10 Jiu, Quansen 10 Li, Jinkai 10 Qu, Changzheng 10 Zhang, Zhifei 9 Gao, Hongjun 9 Kukavica, Igor 9 Li, Shan 9 Wang, Shu 9 Wang, Yinxia 8 Au, Vo Van 8 Dong, Boqing 8 Glatt-Holtz, Nathan E. 8 Hieber, Matthias 8 Li, Yongsheng 8 Qian, Chenyin 8 Shang, Haifeng 8 Wang, Yuzhu 8 Yu, Xinwei 7 Fan, Jishan 7 Gal, Ciprian Gheorghe Sorin 7 Guo, Boling 7 Li, Fang 7 Lin, Hongxia 6 Jia, Xuanji 6 Liu, Jitao 6 Ma, Liangliang 6 Yao, Zhengan 6 Zhang, Guodong 6 Zhang, Ping 6 Zhang, Ting 6 Zhu, Mingxuan 5 Bian, Dongfen 5 Can, Nguyen Huu 5 Hussein, Amru 5 Ji, Ruihong 5 Jia, Yan 5 Kashiwabara, Takahito 5 Larios, Adam 5 Lei, Zhen 5 Liu, Xiaochuan 5 Lunasin, Evelyn M. 5 Nakamura, Gen 5 Petcu, Madalina 5 Petronilho, Gerson 5 Tran, Chuong V. 5 Wang, Wendong 5 Xiang, Zhaoyin 5 Xu, Fuyi 5 Yan, Wei 5 Ye, Zhuan 5 Zajączkowski, Wojciech M. 5 Zhong, Dingxing 5 Ziane, Mohammed 4 Adhikari, Dhanapati 4 Barostichi, Rafael F. 4 Biswas, Animikh 4 Fang, Daoyuan 4 Farhat, Aseel 4 Fu, Ying 4 Grasselli, Maurizio 4 Gui, Guilong 4 Guo, Fei 4 Hu, Weiwei 4 Huang, Daiwen 4 Jiang, Zaihong 4 Kobel’kov, Georgiĭ Mikhaĭlovich 4 Li, Fucai 4 Lu, Ming 4 Miranville, Alain M. 4 Pokorný, Milan 4 Qin, Yuming 4 Sun, Chengfeng 4 Tan, Zhong 4 Tang, Tong 4 Wang, Cheng 4 Yang, Jinjin 4 Ye, Xia 4 Yu, Yanghai ...and 641 more Authors
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#### Cited in 144 Serials

 72 Journal of Mathematical Analysis and Applications 63 Journal of Differential Equations 38 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 38 Nonlinear Analysis. Real World Applications 31 Journal of Mathematical Physics 30 Journal of Mathematical Fluid Mechanics 28 Applied Mathematics Letters 25 Computers & Mathematics with Applications 24 ZAMP. Zeitschrift für angewandte Mathematik und Physik 23 Discrete and Continuous Dynamical Systems 21 Mathematical Methods in the Applied Sciences 17 Archive for Rational Mechanics and Analysis 15 Applicable Analysis 14 SIAM Journal on Mathematical Analysis 14 Abstract and Applied Analysis 13 Communications in Mathematical Physics 13 Communications on Pure and Applied Analysis 12 Journal of Nonlinear Science 11 Journal of Functional Analysis 10 Acta Applicandae Mathematicae 10 Physica D 10 Boundary Value Problems 9 Discrete and Continuous Dynamical Systems. Series B 8 Nonlinearity 8 Applied Mathematics and Computation 7 Chinese Annals of Mathematics. Series B 7 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Advances in Mathematics 6 Science China. Mathematics 5 Annales Polonici Mathematici 5 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 5 Analysis and Applications (Singapore) 5 Kinetic and Related Models 4 Journal of Statistical Physics 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Applied Mathematics and Optimization 4 Numerische Mathematik 4 SIAM Journal on Numerical Analysis 4 Stochastic Analysis and Applications 4 Journal of Scientific Computing 4 Discrete and Continuous Dynamical Systems. Series S 3 Computer Methods in Applied Mechanics and Engineering 3 Communications on Pure and Applied Mathematics 3 Journal of Computational and Applied Mathematics 3 Applied Numerical Mathematics 3 Applications of Mathematics 3 Communications in Partial Differential Equations 3 Journal of Evolution Equations 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Stochastics and Dynamics 3 Bulletin of the Brazilian Mathematical Society. New Series 2 Journal of Computational Physics 2 Journal of Fluid Mechanics 2 Proceedings of the American Mathematical Society 2 SIAM Journal on Control and Optimization 2 Acta Mathematicae Applicatae Sinica. English Series 2 Computational Mechanics 2 Geometric and Functional Analysis. GAFA 2 Journal of Dynamics and Differential Equations 2 SIAM Journal on Scientific Computing 2 Calculus of Variations and Partial Differential Equations 2 Engineering Analysis with Boundary Elements 2 Doklady Mathematics 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Mathematical Physics, Analysis and Geometry 2 Journal of Inequalities and Applications 2 Acta Mathematica Sinica. English Series 2 Communications in Contemporary Mathematics 2 Acta Mathematica Scientia. Series B. (English Edition) 2 Mediterranean Journal of Mathematics 2 Frontiers of Mathematics in China 2 Analysis & PDE 2 Differential Equations and Applications 2 Advances in Mathematical Physics 2 Journal of Geometric Mechanics 2 Evolution Equations and Control Theory 2 Advances in Nonlinear Analysis 2 Journal of Function Spaces 2 Mathematics of Climate and Weather Forecasting 1 Acta Mechanica 1 Journal d’Analyse Mathématique 1 Mathematical Notes 1 Rocky Mountain Journal of Mathematics 1 Mathematics of Computation 1 Journal of Geometry and Physics 1 Indiana University Mathematics Journal 1 Mathematische Annalen 1 Mathematische Nachrichten 1 Mathematische Zeitschrift 1 Monatshefte für Mathematik 1 Numerical Functional Analysis and Optimization 1 Osaka Journal of Mathematics 1 Pacific Journal of Mathematics 1 Results in Mathematics 1 Ricerche di Matematica 1 Studies in Applied Mathematics 1 Tokyo Journal of Mathematics 1 Transactions of the Moscow Mathematical Society 1 Systems & Control Letters 1 Bulletin of the Korean Mathematical Society ...and 44 more Serials
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#### Cited in 33 Fields

 717 Partial differential equations (35-XX) 583 Fluid mechanics (76-XX) 114 Geophysics (86-XX) 60 Dynamical systems and ergodic theory (37-XX) 49 Numerical analysis (65-XX) 33 Harmonic analysis on Euclidean spaces (42-XX) 32 Probability theory and stochastic processes (60-XX) 19 Real functions (26-XX) 16 Systems theory; control (93-XX) 14 Operator theory (47-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 11 Ordinary differential equations (34-XX) 9 Mechanics of deformable solids (74-XX) 9 Classical thermodynamics, heat transfer (80-XX) 8 Optics, electromagnetic theory (78-XX) 5 Functional analysis (46-XX) 4 Integral equations (45-XX) 4 Astronomy and astrophysics (85-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Measure and integration (28-XX) 2 Functions of a complex variable (30-XX) 2 Potential theory (31-XX) 2 Special functions (33-XX) 2 Differential geometry (53-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Approximations and expansions (41-XX) 1 Manifolds and cell complexes (57-XX) 1 Relativity and gravitational theory (83-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX)