Edit Profile (opens in new tab) Doering, Charles Rogers Compute Distance To: Compute Author ID: doering.charles-r Published as: Doering, Charles R.; Doering, C. R.; Doering, Charles; Doering, C. Homepage: http://www.lsa.umich.edu/math/people?uniqname=doering External Links: MGP · ORCID · Wikidata · dblp · GND · IdRef Documents Indexed: 103 Publications since 1987, including 1 Book 1 Contribution as Editor Biographic References: 1 Publication Co-Authors: 111 Co-Authors with 99 Joint Publications 2,565 Co-Co-Authors all top 5 Co-Authors 5 single-authored 16 Gibbon, John D. 7 Constantin, Peter 6 Thiffeault, Jean-Luc 5 Eckhardt, Bruno 5 Goluskin, David 4 Chini, Gregory P. 4 Lin, Zhi 4 Schumacher, Jörg 4 Worthing, Rodney A. 3 Holm, Darryl D. 3 Kim, Hyejin 3 Levermore, C. David 3 Lin, Yen Ting 3 Lu, Lu 3 Lunasin, Evelyn M. 3 Mazzucato, Anna L. 3 Souza, Andre N. 3 Spiegel, Edward A. 3 Titi, Edriss Saleh 3 Tobasco, Ian 3 Wen, Baole 3 Whitehead, Jared P. 2 Bartuccelli, Michele V. 2 Bod’ová, Katarína 2 Burschka, Martin A. 2 Dianati, Navid 2 Dontcheva, Lubomira A. 2 Gallet, Basile 2 Hagan, Patrick S. 2 Johnston, Hans 2 Kurganov, Alexander 2 Miles, Christopher J. 2 Nicolaenko, Basil 2 Novikov, Alexei 2 Otero, Jesse 2 Sander, Leonard M. 2 Sargsyan, Khachik V. 2 Shaw, Tiffany A. 2 Smereka, Peter 1 Abbott, Derek 1 Alexakis, Alexandros 1 Ayala, Diego 1 Balci, Nusret 1 Bartucelli, M. V. 1 ben-Avraham, Daniel 1 Ben-Naim, Eli 1 Bezrukov, Sergey M. 1 Bowman, John C. 1 Brandt, Howard Edward 1 Busse, Friedrich Hermann 1 Caves, Carlton M. 1 Chakraborty, Bulbul 1 Chertock, Alina E. 1 Cheskidov, Alexey 1 Conlon, Joseph G. 1 Davoudi, Jahanshah 1 Dubief, Yves 1 Ferry, David K. 1 Foiaş, Ciprian Ilie 1 Fokas, Athanassios S. 1 Gammack, David 1 Gaveau, Bernard 1 Gea-Banacloche, Julio 1 Gisselfält, Magnus 1 Glauser, Mark 1 Goldburg, Walter I. 1 Hagstrom, George I. 1 Hamilton, Alex R. 1 Hassanzadeh, Pedram 1 Horsthemke, Werner 1 Kashdan, Eugene 1 Kim, Seunghwan 1 Kirschner, Denise E. 1 Kish, Laszlo B. 1 Kłosek, Małgorzata M. 1 Kukavica, Igor 1 Lathrop, Daniel P. 1 Leduc, Matthew 1 Lidar, Daniel M. 1 Malham, Simon J. A. 1 Marcotte, Florence 1 McMillan, Andrew N. 1 Müller, Carl E. 1 Newton, Paul K. 1 Olson, Matthew L. 1 Otto, Felix 1 Park, Seon Hee 1 Petrov, Nikola P. 1 Petrova, Guergana 1 Redner, Sidney 1 Renardy, Michael 1 Reznikoff, Maria G. 1 Roberts, Malcolm 1 Rollin, Bertrand 1 Ryu, Chang Su 1 Schulman, Lawrence S. 1 Schultz, William W. 1 Simon, Thilo M. 1 Thomases, Becca 1 Toppaladoddi, Srikanth ...and 11 more Co-Authors all top 5 Serials 21 Journal of Fluid Mechanics 16 Physica D 9 Journal of Mathematical Physics 7 Physics Letters. A 6 Journal of Statistical Physics 5 Nonlinearity 4 Chaos 3 Journal of Mathematical Biology 3 Physics of Fluids 2 Journal of Non-Newtonian Fluid Mechanics 2 SIAM Journal on Applied Mathematics 2 Journal of Nonlinear Science 1 Archive for Rational Mechanics and Analysis 1 Communications in Mathematical Physics 1 Communications on Pure and Applied Mathematics 1 Physica A 1 Indiana University Mathematics Journal 1 Theoretical Population Biology 1 Dynamics and Stability of Systems 1 Journal of Scientific Computing 1 Journal of Physics A: Mathematical and General 1 Proceedings of the National Academy of Sciences of the United States of America 1 Discrete and Continuous Dynamical Systems 1 Multiscale Modeling & Simulation 1 Quantum Information Processing 1 Communications in Mathematical Sciences 1 Pure and Applied Functional Analysis 1 Cambridge Texts in Applied Mathematics all top 5 Fields 73 Fluid mechanics (76-XX) 33 Partial differential equations (35-XX) 17 Classical thermodynamics, heat transfer (80-XX) 14 Dynamical systems and ergodic theory (37-XX) 11 Probability theory and stochastic processes (60-XX) 7 Numerical analysis (65-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Biology and other natural sciences (92-XX) 4 Quantum theory (81-XX) 3 Ordinary differential equations (34-XX) 2 General and overarching topics; collections (00-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Mechanics of particles and systems (70-XX) 2 Mechanics of deformable solids (74-XX) 1 History and biography (01-XX) 1 Difference and functional equations (39-XX) 1 Operator theory (47-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 90 Publications have been cited 1,522 times in 971 Documents Cited by ▼ Year ▼ Applied analysis of the Navier-Stokes equations. Zbl 0838.76016Doering, Charles R.; Gibbon, J. D. 179 1995 Low-dimensional behaviour in the complex Ginzburg-Landau equation. Zbl 0655.58021Doering, Charles R.; Gibbon, John D.; Holm, Darryl D.; Nicolaenko, Basil 95 1988 Weak and strong solutions of the complex Ginzburg-Landau equation. Zbl 0810.35119Doering, Charles R.; Gibbon, John D.; Levermore, C. David 92 1994 On the possibility of soft and hard turbulence in the complex Ginzburg- Landau equation. Zbl 0702.76061Bartuccelli, Michele; Constantin, Petre; Doering, Charles R.; Gibbon, John D.; Gisselfält, Magnus 61 1990 Infinite Prandtl number convection. Zbl 0935.76083Constantin, Peter; Doering, Charles R. 58 1999 Energy dissipation in body-forced turbulence. Zbl 1029.76025Doering, Charles R.; Foias, Ciprian 56 2002 Extinction times for birth-death processes: Exact results, continuum asymptotics, and the failure of the Fokker-Planck approximation. Zbl 1072.60092Doering, Charles R.; Sargsyan, Khachik V.; Sander, Leonard M. 53 2005 Optimal stirring strategies for passive scalar mixing. Zbl 1241.76361Lin, Zhi; Thiffeault, Jean-Luc; Doering, Charles R. 51 2011 Bounds on vertical heat transport for infinite-Prandtl-number Rayleigh–Bénard convection. Zbl 1122.76080Doering, Charles R.; Otto, Felix; Reznikoff, Maria G. 39 2006 Exponential decay rate of the power spectrum for solutions of the Navier-Stokes equations. Zbl 1023.76513Doering, Charles R.; Titi, Edriss S. 37 1995 High-Rayleigh-number convection in a fluid-saturated porous layer. Zbl 1134.76462Otero, Jesse; Dontcheva, Lubomira A.; Johnston, Hans; Worthing, Rodney A.; Kurganov, Alexander; Petrova, Guergana; Doering, Charles R. 32 2004 Long time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion. Zbl 1398.35164Doering, Charles R.; Wu, Jiahong; Zhao, Kun; Zheng, Xiaoming 31 2018 On upper bounds for infinite Prandtl number convection with or without rotation. Zbl 1061.76520Doering, Charles R.; Constantin, Peter 30 2001 Bounds on Rayleigh-Bénard convection with an imposed heat flux. Zbl 1026.76048Otero, Jesse; Wittenberg, Ralf W.; Worthing, Rodney A.; Doering, Charles R. 29 2002 Heat transfer in convective turbulence. Zbl 0899.35078Constantin, Peter; Doering, Charles R. 26 1996 Wall to wall optimal transport. Zbl 1329.74253Hassanzadeh, Pedram; Chini, Gregory P.; Doering, Charles R. 25 2014 The 3D Navier-Stokes problem. Zbl 1157.76008Doering, Charles R. 24 2009 Optimal mixing and optimal stirring for fixed energy, fixed power, or fixed palenstrophy flows. Zbl 1302.76076Lunasin, Evelyn; Lin, Zhi; Novikov, Alexei; Mazzucato, Anna; Doering, Charles R. 22 2012 Interacting particles, the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation, and duality. Zbl 1025.60027Doering, Charles R.; Mueller, Carl; Smereka, Peter 21 2003 A bound on mixing efficiency for the advection-diffusion equation. Zbl 1065.76184Thiffeault, Jean-Luc; Doering, Charles R.; Gibbon, John D. 21 2004 Dynamically stretched vortices as solutions of the 3D Navier-Stokes equations. Zbl 0956.76018Gibbon, J. D.; Fokas, A. S.; Doering, C. R. 21 1999 Limits on enstrophy growth for solutions of the three-dimensional Navier-Stokes equations. Zbl 1172.35055Lu, Lu; Doering, Charles R. 19 2008 Bounds for heat transport in a porous layer. Zbl 0933.76090Doering, Charles R.; Constantin, Peter 18 1998 Statics and dynamics of a diffusion-limited reaction: anomalous kinetics, nonequilibrium self-ordering, and a dynamic transition. Zbl 1086.82556ben-Avraham, Daniel; Burschka, Martin A.; Doering, Charles R. 18 1990 Failure of energy stability in Oldroyd-B fluids at arbitrarily low Reynolds numbers. Zbl 1195.76174Doering, Charles R.; Eckhardt, Bruno; Schumacher, Jörg 17 2006 Stirring up trouble: multi-scale mixing measures for steady scalar sources. Zbl 1128.35087Shaw, Tiffany A.; Thiffeault, Jean-Luc; Doering, Charles R. 17 2007 Energy dissipation in a shear layer with suction. Zbl 1184.76140Doering, Charles R.; Spiegel, Edward A.; Worthing, Rodney A. 16 2000 Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems. Zbl 1383.37001Tobasco, Ian; Goluskin, David; Doering, Charles R. 15 2018 Rigid bounds on heat transport by a fluid between slippery boundaries. Zbl 1275.76192Whitehead, Jared P.; Doering, Charles R. 15 2012 On travelling waves for the stochastic Fisher-Kolmogorov-Petrovsky-Piscunov equation. Zbl 1095.82008Conlon, Joseph G.; Doering, Charles R. 15 2005 Energy and enstrophy dissipation in steady state 2d turbulence. Zbl 1236.76029Alexakis, Alexandros; Doering, Charles R. 15 2006 Length scales in solutions of the Navier-Stokes equations. Zbl 0782.35056Bartucelli, M. V.; Doering, C. R.; Gibbon, J. D.; Malham, S. J. A. 15 1993 On the shape and dimension of the Lorenz attractor. Zbl 0838.34070Doering, Charles R.; Gibbon, J. D. 14 1995 Internal heating driven convection at infinite Prandtl number. Zbl 1272.76230Whitehead, Jared P.; Doering, Charles R. 14 2011 Mean exit times for particles driven by weakly colored noise. Zbl 0681.60052Hagan, Patrick S.; Doering, Charles R.; Levermore, C. David 14 1989 Computational approaches to aspect-ratio-dependent upper bounds and heat flux in porous medium convection. Zbl 1370.76182Wen, Baole; Chini, Gregory P.; Dianati, Navid; Doering, Charles R. 14 2013 Bounds for convection between rough boundaries. Zbl 1454.76088Goluskin, David; Doering, Charles R. 14 2016 Symmetric factorization of the conformation tensor in viscoelastic fluid models. Zbl 1359.76023Balci, Nusret; Thomases, Becca; Renardy, Michael; Doering, Charles R. 13 2011 Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field. Zbl 1328.76075Gallet, Basile; Doering, Charles R. 13 2015 Variational bounds in dissipative systems. Zbl 0900.35049Constantin, Peter; Doering, Charles 12 1995 Features of fast living: on the weak selection for longevity in degenerate birth-death processes. Zbl 1257.82087Lin, Yen Ting; Kim, Hyejin; Doering, Charles R. 11 2012 Bounds on moments of the energy spectrum for weak solutions of the three-dimensional Navier-Stokes equations. Zbl 0997.35046Doering, Charles R.; Gibbon, J. D. 10 2002 The distribution of exit times for weakly colored noise. Zbl 0714.60072Hagan, Patrick S.; Doering, Charles R.; Levermore, C. David 10 1989 A numerical method for some stochastic differential equations with multiplicative noise. Zbl 1194.65024Doering, Charles R.; Sargsyan, Khachik V.; Smereka, Peter 10 2005 Extreme vorticity growth in Navier-Stokes turbulence. Zbl 1235.76030Schumacher, Jörg; Eckhardt, Bruno; Doering, Charles R. 9 2010 Energy dissipation in body-forced plane shear flow. Zbl 1051.76028Doering, C. R.; Eckhardt, B.; Schumacher, J. 9 2003 Bounds on convection driven by internal heating. Zbl 1071.76027Lu, Lu; Doering, Charles R.; Busse, Friedrich H. 9 2004 Note on the Constantin-Foias-Temam attractor dimension estimate for two- dimensional turbulence. Zbl 0728.76030Doering, Charles R.; Gibbon, John D. 9 1991 Diffusion-limited mixing by incompressible flows. Zbl 1390.76840Miles, Christopher J.; Doering, Charles R. 8 2018 Intermittency and regularity issues in \(3D\) Navier-Stokes turbulence. Zbl 1129.76014Gibbon, J. D.; Doering, Charles R. 7 2005 A fast explicit operator splitting method for passive scalar advection. Zbl 1203.76126Chertock, Alina; Doering, Charles R.; Kashdan, Eugene; Kurganov, Alexander 7 2010 On the optimal design of wall-to-wall heat transport. Zbl 1434.76036Doering, Charles R.; Tobasco, Ian 7 2019 Transport bounds for a truncated model of Rayleigh-Bénard convection. Zbl 1364.76056Souza, Andre N.; Doering, Charles R. 7 2015 Steady Rayleigh-Bénard convection between stress-free boundaries. Zbl 1460.76322Wen, Baole; Goluskin, David; Leduc, Matthew; Chini, Gregory P.; Doering, Charles R. 6 2020 Macrophage response to Mycobacterium tuberculosis infection. Zbl 1058.92026Gammack, D.; Doering, C. R.; Kirschner, D. E. 6 2004 Nonlinear parabolic stochastic differential equations with additive colored noise on \({\mathbb{R}}^ d\times {\mathbb{R}}_ +:\) A regulated stochastic quantization. Zbl 0625.60069Doering, Charles R. 6 1987 Rigorous estimates of small scales in turbulent flows. Zbl 0862.35083Constantin, Peter; Doering, Charles R.; Titi, Edriss S. 6 1996 Energy dissipation in fractal-forced flow. Zbl 1144.81330Cheskidov, Alexey; Doering, Charles R.; Petrov, Nikola P. 6 2007 Destabilizing Taylor-Couette flow with suction. Zbl 1188.76051Gallet, Basile; Doering, Charles R.; Spiegel, Edward A. 6 2010 Maximal transport in the Lorenz equations. Zbl 1342.80005Souza, Andre N.; Doering, Charles R. 6 2015 Attractor dimension estimates for two-dimensional shear flows. Zbl 0956.76017Doering, Charles R.; Wang, Xiaoming 5 1998 Variations on Kolmogorov flow: turbulent energy dissipation and mean flow profiles. Zbl 1225.76151Rollin, B.; Dubief, Y.; Doering, C. R. 5 2011 Fluctuations and correlations in a diffusion-reaction system: Exact hydrodynamics. Zbl 0946.82516Doering, Charles R.; Burschka, Martin A.; Horsthemke, Werner 4 1991 Links between dissipation, intermittency, and helicity in the GOY model revisited. Zbl 1099.76024Bowman, John C.; Doering, Charles R.; Eckhardt, Bruno; Davoudi, Jahanshah; Roberts, Malcolm; Schumacher, Jörg 4 2006 Intermittency in solutions of the three-dimensional Navier-Stokes equations. Zbl 1034.76013Gibbon, J. D.; Doering, Charles R. 4 2003 Ladder theorems for the \(2D\) and \(3D\) Navier-Stokes equations on a finite periodic domain. Zbl 0736.35084Bartuccelli, M.; Doering, C.; Gibbon, J. D. 4 1991 Bounds on surface stress-driven shear flow. Zbl 1302.76050Hagstrom, George I.; Doering, Charles R. 4 2014 Wall-to-wall optimal transport in two dimensions. Zbl 1460.76728Souza, Andre N.; Tobasco, Ian; Doering, Charles R. 4 2020 Thermal convection over fractal surfaces. Zbl 1461.76247Toppaladoddi, Srikanth; Wells, Andrew J.; Doering, Charles R.; Wettlaufer, John S. 3 2020 Demographic stochasticity versus spatial variation in the competition between fast and slow dispersers. Zbl 1403.92273Waddell, Jack N.; Sander, Leonard M.; Doering, Charles R. 3 2010 Optimal heat transfer and optimal exit times. Zbl 1387.76096Marcotte, Florence; Doering, Charles R.; Thiffeault, Jean-Luc; Young, William R. 3 2018 Finite dimensionality in the complex Ginzburg-Landau equation. Zbl 0741.35079Doering, C. R.; Gibbon, J. D.; Holm, D. D.; Nicolaenko, B. 3 1989 Models & measures of mixing & effective diffusion. Zbl 1387.76038Lin, Zhi; Bod’ová, Katarína; Doering, Charles R. 3 2010 Noise-induced statistically stable oscillations in a deterministically divergent nonlinear dynamical system. Zbl 1274.60177Boďová, Katarína; Doering, Charles 3 2012 Steady Rayleigh-Bénard convection between no-slip boundaries. Zbl 07451559Wen, Baole; Goluskin, David; Doering, Charles R. 3 2022 Demographic stochasticity and evolution of dispersion. II: Spatially inhomogeneous environments. Zbl 1350.92043Lin, Yen Ting; Kim, Hyejin; Doering, Charles R. 2 2015 Thermal forcing and ‘classical’ and ‘ultimate’ regimes of Rayleigh-Bénard convection. Zbl 1415.76309Doering, Charles R. 2 2019 A shell model for optimal mixing. Zbl 1448.76147Miles, Christopher J.; Doering, Charles R. 2 2018 Linear decay in multilevel quantum systems. Zbl 0729.35110Schulman, L. S.; Doering, C. R.; Gaveau, B. 2 1991 Low-dimensional models from upper bound theory. Zbl 1372.37121Chini, Gregory P.; Dianati, Navid; Zhang, Zhexuan; Doering, Charles R. 2 2011 Constructive role of noise: Fast fluctuation asymptotics of transport in stochastic ratchets. Zbl 0988.70018Doering, Charles R.; Dontcheva, Lubomira A.; Klosek, Malgorzata M. 2 1998 Maximum palinstrophy amplification in the two-dimensional Navier-Stokes equations. Zbl 1419.76127Ayala, Diego; Doering, Charles R.; Simon, Thilo M. 1 2018 Exact relations between Rayleigh-Bénard and rotating plane Couette flow in two dimensions. Zbl 1460.76732Eckhardt, Bruno; Doering, Charles R.; Whitehead, Jared P. 1 2020 Demographic stochasticity and evolution of dispersion. I: Spatially homogeneous environments. Zbl 1350.92042Lin, Yen Ting; Kim, Hyejin; Doering, Charles R. 1 2015 Erratum: “Optimal mixing and optimal stirring for fixed energy, fixed power, or fixed palenstrophy flows”. Zbl 1302.76077Lunasin, Evelyn; Lin, Zhi; Novikov, Alexei; Mazzucato, Anna; Doering, Charles R. 1 2013 Rayleigh-Bénard convection with imposed heat flux. Zbl 1163.37340Johnston, Hans; Doering, Charles R. 1 2007 The dynamics of organized structures in the axisymmetric jet mixing layer. Zbl 0728.76056Glauser, Mark; Zheng, Xiaowei; Doering, Charles R. 1 1991 Laminar and turbulent dissipation in shear flow with suction. Zbl 1035.76022Doering, Charles R.; Spiegel, Edward A.; Worthing, Rodney A. 1 2000 Reentrant transitions in globally coupled active rotators with multiplicative and additive noises. Zbl 0962.82523Kim, Seunghwan; Park, Seon Hee; Doering, Charles R.; Ryu, Chang Su 1 1997 The mixing efficiency of open flows. Zbl 1372.76058Thiffeault, Jean-Luc; Doering, Charles R. 1 2011 Steady Rayleigh-Bénard convection between no-slip boundaries. Zbl 07451559Wen, Baole; Goluskin, David; Doering, Charles R. 3 2022 Steady Rayleigh-Bénard convection between stress-free boundaries. Zbl 1460.76322Wen, Baole; Goluskin, David; Leduc, Matthew; Chini, Gregory P.; Doering, Charles R. 6 2020 Wall-to-wall optimal transport in two dimensions. Zbl 1460.76728Souza, Andre N.; Tobasco, Ian; Doering, Charles R. 4 2020 Thermal convection over fractal surfaces. Zbl 1461.76247Toppaladoddi, Srikanth; Wells, Andrew J.; Doering, Charles R.; Wettlaufer, John S. 3 2020 Exact relations between Rayleigh-Bénard and rotating plane Couette flow in two dimensions. Zbl 1460.76732Eckhardt, Bruno; Doering, Charles R.; Whitehead, Jared P. 1 2020 On the optimal design of wall-to-wall heat transport. Zbl 1434.76036Doering, Charles R.; Tobasco, Ian 7 2019 Thermal forcing and ‘classical’ and ‘ultimate’ regimes of Rayleigh-Bénard convection. Zbl 1415.76309Doering, Charles R. 2 2019 Long time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion. Zbl 1398.35164Doering, Charles R.; Wu, Jiahong; Zhao, Kun; Zheng, Xiaoming 31 2018 Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems. Zbl 1383.37001Tobasco, Ian; Goluskin, David; Doering, Charles R. 15 2018 Diffusion-limited mixing by incompressible flows. Zbl 1390.76840Miles, Christopher J.; Doering, Charles R. 8 2018 Optimal heat transfer and optimal exit times. Zbl 1387.76096Marcotte, Florence; Doering, Charles R.; Thiffeault, Jean-Luc; Young, William R. 3 2018 A shell model for optimal mixing. Zbl 1448.76147Miles, Christopher J.; Doering, Charles R. 2 2018 Maximum palinstrophy amplification in the two-dimensional Navier-Stokes equations. Zbl 1419.76127Ayala, Diego; Doering, Charles R.; Simon, Thilo M. 1 2018 Bounds for convection between rough boundaries. Zbl 1454.76088Goluskin, David; Doering, Charles R. 14 2016 Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field. Zbl 1328.76075Gallet, Basile; Doering, Charles R. 13 2015 Transport bounds for a truncated model of Rayleigh-Bénard convection. Zbl 1364.76056Souza, Andre N.; Doering, Charles R. 7 2015 Maximal transport in the Lorenz equations. Zbl 1342.80005Souza, Andre N.; Doering, Charles R. 6 2015 Demographic stochasticity and evolution of dispersion. II: Spatially inhomogeneous environments. Zbl 1350.92043Lin, Yen Ting; Kim, Hyejin; Doering, Charles R. 2 2015 Demographic stochasticity and evolution of dispersion. I: Spatially homogeneous environments. Zbl 1350.92042Lin, Yen Ting; Kim, Hyejin; Doering, Charles R. 1 2015 Wall to wall optimal transport. Zbl 1329.74253Hassanzadeh, Pedram; Chini, Gregory P.; Doering, Charles R. 25 2014 Bounds on surface stress-driven shear flow. Zbl 1302.76050Hagstrom, George I.; Doering, Charles R. 4 2014 Computational approaches to aspect-ratio-dependent upper bounds and heat flux in porous medium convection. Zbl 1370.76182Wen, Baole; Chini, Gregory P.; Dianati, Navid; Doering, Charles R. 14 2013 Erratum: “Optimal mixing and optimal stirring for fixed energy, fixed power, or fixed palenstrophy flows”. Zbl 1302.76077Lunasin, Evelyn; Lin, Zhi; Novikov, Alexei; Mazzucato, Anna; Doering, Charles R. 1 2013 Optimal mixing and optimal stirring for fixed energy, fixed power, or fixed palenstrophy flows. Zbl 1302.76076Lunasin, Evelyn; Lin, Zhi; Novikov, Alexei; Mazzucato, Anna; Doering, Charles R. 22 2012 Rigid bounds on heat transport by a fluid between slippery boundaries. Zbl 1275.76192Whitehead, Jared P.; Doering, Charles R. 15 2012 Features of fast living: on the weak selection for longevity in degenerate birth-death processes. Zbl 1257.82087Lin, Yen Ting; Kim, Hyejin; Doering, Charles R. 11 2012 Noise-induced statistically stable oscillations in a deterministically divergent nonlinear dynamical system. Zbl 1274.60177Boďová, Katarína; Doering, Charles 3 2012 Optimal stirring strategies for passive scalar mixing. Zbl 1241.76361Lin, Zhi; Thiffeault, Jean-Luc; Doering, Charles R. 51 2011 Internal heating driven convection at infinite Prandtl number. Zbl 1272.76230Whitehead, Jared P.; Doering, Charles R. 14 2011 Symmetric factorization of the conformation tensor in viscoelastic fluid models. Zbl 1359.76023Balci, Nusret; Thomases, Becca; Renardy, Michael; Doering, Charles R. 13 2011 Variations on Kolmogorov flow: turbulent energy dissipation and mean flow profiles. Zbl 1225.76151Rollin, B.; Dubief, Y.; Doering, C. R. 5 2011 Low-dimensional models from upper bound theory. Zbl 1372.37121Chini, Gregory P.; Dianati, Navid; Zhang, Zhexuan; Doering, Charles R. 2 2011 The mixing efficiency of open flows. Zbl 1372.76058Thiffeault, Jean-Luc; Doering, Charles R. 1 2011 Extreme vorticity growth in Navier-Stokes turbulence. Zbl 1235.76030Schumacher, Jörg; Eckhardt, Bruno; Doering, Charles R. 9 2010 A fast explicit operator splitting method for passive scalar advection. Zbl 1203.76126Chertock, Alina; Doering, Charles R.; Kashdan, Eugene; Kurganov, Alexander 7 2010 Destabilizing Taylor-Couette flow with suction. Zbl 1188.76051Gallet, Basile; Doering, Charles R.; Spiegel, Edward A. 6 2010 Demographic stochasticity versus spatial variation in the competition between fast and slow dispersers. Zbl 1403.92273Waddell, Jack N.; Sander, Leonard M.; Doering, Charles R. 3 2010 Models & measures of mixing & effective diffusion. Zbl 1387.76038Lin, Zhi; Bod’ová, Katarína; Doering, Charles R. 3 2010 The 3D Navier-Stokes problem. Zbl 1157.76008Doering, Charles R. 24 2009 Limits on enstrophy growth for solutions of the three-dimensional Navier-Stokes equations. Zbl 1172.35055Lu, Lu; Doering, Charles R. 19 2008 Stirring up trouble: multi-scale mixing measures for steady scalar sources. Zbl 1128.35087Shaw, Tiffany A.; Thiffeault, Jean-Luc; Doering, Charles R. 17 2007 Energy dissipation in fractal-forced flow. Zbl 1144.81330Cheskidov, Alexey; Doering, Charles R.; Petrov, Nikola P. 6 2007 Rayleigh-Bénard convection with imposed heat flux. Zbl 1163.37340Johnston, Hans; Doering, Charles R. 1 2007 Bounds on vertical heat transport for infinite-Prandtl-number Rayleigh–Bénard convection. Zbl 1122.76080Doering, Charles R.; Otto, Felix; Reznikoff, Maria G. 39 2006 Failure of energy stability in Oldroyd-B fluids at arbitrarily low Reynolds numbers. Zbl 1195.76174Doering, Charles R.; Eckhardt, Bruno; Schumacher, Jörg 17 2006 Energy and enstrophy dissipation in steady state 2d turbulence. Zbl 1236.76029Alexakis, Alexandros; Doering, Charles R. 15 2006 Links between dissipation, intermittency, and helicity in the GOY model revisited. Zbl 1099.76024Bowman, John C.; Doering, Charles R.; Eckhardt, Bruno; Davoudi, Jahanshah; Roberts, Malcolm; Schumacher, Jörg 4 2006 Extinction times for birth-death processes: Exact results, continuum asymptotics, and the failure of the Fokker-Planck approximation. Zbl 1072.60092Doering, Charles R.; Sargsyan, Khachik V.; Sander, Leonard M. 53 2005 On travelling waves for the stochastic Fisher-Kolmogorov-Petrovsky-Piscunov equation. Zbl 1095.82008Conlon, Joseph G.; Doering, Charles R. 15 2005 A numerical method for some stochastic differential equations with multiplicative noise. Zbl 1194.65024Doering, Charles R.; Sargsyan, Khachik V.; Smereka, Peter 10 2005 Intermittency and regularity issues in \(3D\) Navier-Stokes turbulence. Zbl 1129.76014Gibbon, J. D.; Doering, Charles R. 7 2005 High-Rayleigh-number convection in a fluid-saturated porous layer. Zbl 1134.76462Otero, Jesse; Dontcheva, Lubomira A.; Johnston, Hans; Worthing, Rodney A.; Kurganov, Alexander; Petrova, Guergana; Doering, Charles R. 32 2004 A bound on mixing efficiency for the advection-diffusion equation. Zbl 1065.76184Thiffeault, Jean-Luc; Doering, Charles R.; Gibbon, John D. 21 2004 Bounds on convection driven by internal heating. Zbl 1071.76027Lu, Lu; Doering, Charles R.; Busse, Friedrich H. 9 2004 Macrophage response to Mycobacterium tuberculosis infection. Zbl 1058.92026Gammack, D.; Doering, C. R.; Kirschner, D. E. 6 2004 Interacting particles, the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation, and duality. Zbl 1025.60027Doering, Charles R.; Mueller, Carl; Smereka, Peter 21 2003 Energy dissipation in body-forced plane shear flow. Zbl 1051.76028Doering, C. R.; Eckhardt, B.; Schumacher, J. 9 2003 Intermittency in solutions of the three-dimensional Navier-Stokes equations. Zbl 1034.76013Gibbon, J. D.; Doering, Charles R. 4 2003 Energy dissipation in body-forced turbulence. Zbl 1029.76025Doering, Charles R.; Foias, Ciprian 56 2002 Bounds on Rayleigh-Bénard convection with an imposed heat flux. Zbl 1026.76048Otero, Jesse; Wittenberg, Ralf W.; Worthing, Rodney A.; Doering, Charles R. 29 2002 Bounds on moments of the energy spectrum for weak solutions of the three-dimensional Navier-Stokes equations. Zbl 0997.35046Doering, Charles R.; Gibbon, J. D. 10 2002 On upper bounds for infinite Prandtl number convection with or without rotation. Zbl 1061.76520Doering, Charles R.; Constantin, Peter 30 2001 Energy dissipation in a shear layer with suction. Zbl 1184.76140Doering, Charles R.; Spiegel, Edward A.; Worthing, Rodney A. 16 2000 Laminar and turbulent dissipation in shear flow with suction. Zbl 1035.76022Doering, Charles R.; Spiegel, Edward A.; Worthing, Rodney A. 1 2000 Infinite Prandtl number convection. Zbl 0935.76083Constantin, Peter; Doering, Charles R. 58 1999 Dynamically stretched vortices as solutions of the 3D Navier-Stokes equations. Zbl 0956.76018Gibbon, J. D.; Fokas, A. S.; Doering, C. R. 21 1999 Bounds for heat transport in a porous layer. Zbl 0933.76090Doering, Charles R.; Constantin, Peter 18 1998 Attractor dimension estimates for two-dimensional shear flows. Zbl 0956.76017Doering, Charles R.; Wang, Xiaoming 5 1998 Constructive role of noise: Fast fluctuation asymptotics of transport in stochastic ratchets. Zbl 0988.70018Doering, Charles R.; Dontcheva, Lubomira A.; Klosek, Malgorzata M. 2 1998 Reentrant transitions in globally coupled active rotators with multiplicative and additive noises. Zbl 0962.82523Kim, Seunghwan; Park, Seon Hee; Doering, Charles R.; Ryu, Chang Su 1 1997 Heat transfer in convective turbulence. Zbl 0899.35078Constantin, Peter; Doering, Charles R. 26 1996 Rigorous estimates of small scales in turbulent flows. Zbl 0862.35083Constantin, Peter; Doering, Charles R.; Titi, Edriss S. 6 1996 Applied analysis of the Navier-Stokes equations. Zbl 0838.76016Doering, Charles R.; Gibbon, J. D. 179 1995 Exponential decay rate of the power spectrum for solutions of the Navier-Stokes equations. Zbl 1023.76513Doering, Charles R.; Titi, Edriss S. 37 1995 On the shape and dimension of the Lorenz attractor. Zbl 0838.34070Doering, Charles R.; Gibbon, J. D. 14 1995 Variational bounds in dissipative systems. Zbl 0900.35049Constantin, Peter; Doering, Charles 12 1995 Weak and strong solutions of the complex Ginzburg-Landau equation. Zbl 0810.35119Doering, Charles R.; Gibbon, John D.; Levermore, C. David 92 1994 Length scales in solutions of the Navier-Stokes equations. Zbl 0782.35056Bartucelli, M. V.; Doering, C. R.; Gibbon, J. D.; Malham, S. J. A. 15 1993 Note on the Constantin-Foias-Temam attractor dimension estimate for two- dimensional turbulence. Zbl 0728.76030Doering, Charles R.; Gibbon, John D. 9 1991 Fluctuations and correlations in a diffusion-reaction system: Exact hydrodynamics. Zbl 0946.82516Doering, Charles R.; Burschka, Martin A.; Horsthemke, Werner 4 1991 Ladder theorems for the \(2D\) and \(3D\) Navier-Stokes equations on a finite periodic domain. Zbl 0736.35084Bartuccelli, M.; Doering, C.; Gibbon, J. D. 4 1991 Linear decay in multilevel quantum systems. Zbl 0729.35110Schulman, L. S.; Doering, C. R.; Gaveau, B. 2 1991 The dynamics of organized structures in the axisymmetric jet mixing layer. Zbl 0728.76056Glauser, Mark; Zheng, Xiaowei; Doering, Charles R. 1 1991 On the possibility of soft and hard turbulence in the complex Ginzburg- Landau equation. Zbl 0702.76061Bartuccelli, Michele; Constantin, Petre; Doering, Charles R.; Gibbon, John D.; Gisselfält, Magnus 61 1990 Statics and dynamics of a diffusion-limited reaction: anomalous kinetics, nonequilibrium self-ordering, and a dynamic transition. Zbl 1086.82556ben-Avraham, Daniel; Burschka, Martin A.; Doering, Charles R. 18 1990 Mean exit times for particles driven by weakly colored noise. Zbl 0681.60052Hagan, Patrick S.; Doering, Charles R.; Levermore, C. David 14 1989 The distribution of exit times for weakly colored noise. Zbl 0714.60072Hagan, Patrick S.; Doering, Charles R.; Levermore, C. David 10 1989 Finite dimensionality in the complex Ginzburg-Landau equation. Zbl 0741.35079Doering, C. R.; Gibbon, J. D.; Holm, D. D.; Nicolaenko, B. 3 1989 Low-dimensional behaviour in the complex Ginzburg-Landau equation. Zbl 0655.58021Doering, Charles R.; Gibbon, John D.; Holm, Darryl D.; Nicolaenko, Basil 95 1988 Nonlinear parabolic stochastic differential equations with additive colored noise on \({\mathbb{R}}^ d\times {\mathbb{R}}_ +:\) A regulated stochastic quantization. Zbl 0625.60069Doering, Charles R. 6 1987 all cited Publications top 5 cited Publications all top 5 Cited by 1,346 Authors 48 Doering, Charles Rogers 33 Wu, Jiahong 24 Titi, Edriss Saleh 20 Gibbon, John D. 18 Guo, Boling 17 Wang, Xiaoming 16 Jolly, Michael S. 12 Foiaş, Ciprian Ilie 11 Fantuzzi, Giovanni 11 Robinson, James Cooper 10 Bartuccelli, Michele V. 10 Layton, William J. 9 Goluskin, David 9 Thiffeault, Jean-Luc 8 Chini, Gregory P. 8 Constantin, Peter 8 Dascaliuc, Radu 8 Gao, Hongjun 8 Shu, Ji 8 Xu, Xiaojing 7 Alexakis, Alexandros 7 Biswas, Animikh 7 Hu, Weiwei 7 Kerswell, Richard Rodney 7 Whitehead, Jared P. 6 Bedrossian, Jacob 6 Duan, Jinqiao 6 Glatt-Holtz, Nathan E. 6 Levermore, C. David 6 Lu, Shujuan 6 Łukaszewicz, Grzegorz 6 Oliver, Marcel 6 Protas, Bartosz 6 Temam, Roger Meyer 6 Wen, Baole 6 Wynn, Andrew 5 Alarcón, Tomás 5 Boritchev, Alexandre 5 Bu, Charles 5 Coti Zelati, Michele 5 Fang, Tao 5 Gallet, Basile 5 Grujić, Zoran 5 Lunasin, Evelyn M. 5 Mazzucato, Anna L. 5 Morgulis, Andrey Borisovich 5 Ohkitani, Koji 5 Otto, Felix 5 Park, Jungho 5 Schumacher, Jörg 5 Seis, Christian 5 Shishkina, Ol’ga Andreevna 5 Sun, Ji Tao 5 Young, William R. 4 Ayala, Diego 4 Balasuriya, Sanjeeva 4 Camassa, Roberto 4 Cao, Chongsheng 4 Chernyshenko, Sergei I. 4 Clancy, Damian 4 Crippa, Gianluca 4 Doelman, Arjen 4 Donzis, Diego A. 4 Elgindi, Tarek Mohamed 4 Forgoston, Eric 4 Froyland, Gary 4 Gupta, Anupam 4 Hewitt, Duncan R. 4 Hoang, Luan Thach 4 Il’in, Konstantin Ivanovich 4 Iyer, Gautam 4 Kalita, Piotr 4 Kawahara, Genta 4 Kerr, Robert M. 4 Kukavica, Igor 4 Lai, Suhua 4 Leonov, Gennadiĭ Alekseevich 4 Lewandowski, Roger 4 Lohse, Detlef 4 Lu, Hong 4 Martinez, Vincent R. 4 McLaughlin, Richard M. 4 Motoki, Shingo 4 Müller, Carl E. 4 Nobili, Camilla 4 Olson, Eric J. 4 Prudhomme, Serge 4 Renardy, Michael 4 Shang, Haifeng 4 Shimizu, Masaki 4 Sun, Chunyou 4 Verzicco, Roberto 4 Vincenzi, Dario 4 Wang, Baoxiang 4 Wang, Bixiang 4 Ye, Zhuan 4 Zaki, Tamer A. 4 Zhang, Jianwen 3 Arslan, Ali 3 Balci, Nusret ...and 1,246 more Authors all top 5 Cited in 203 Serials 154 Journal of Fluid Mechanics 74 Physica D 36 Journal of Mathematical Physics 33 Journal of Differential Equations 32 Journal of Mathematical Analysis and Applications 31 Physics of Fluids 30 Journal of Statistical Physics 19 Journal of Nonlinear Science 17 Communications in Mathematical Physics 16 Journal of Computational Physics 16 Physics Letters. A 15 Archive for Rational Mechanics and Analysis 15 Journal of Theoretical Biology 14 Applied Mathematics and Computation 12 Journal of Mathematical Biology 12 Discrete and Continuous Dynamical Systems. Series B 11 Nonlinearity 11 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 11 SIAM Journal on Applied Dynamical Systems 10 Applied Mathematics Letters 8 Bulletin of Mathematical Biology 8 Communications in Partial Differential Equations 7 Mathematical Methods in the Applied Sciences 7 Journal of Dynamics and Differential Equations 7 Discrete and Continuous Dynamical Systems 7 Journal of Mathematical Fluid Mechanics 6 Communications on Pure and Applied Mathematics 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 Journal of Functional Analysis 6 Numerical Functional Analysis and Optimization 5 Applicable Analysis 5 Computer Methods in Applied Mechanics and Engineering 5 Applied Mathematics and Mechanics. (English Edition) 5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 Acta Mathematicae Applicatae Sinica. English Series 5 Probability Theory and Related Fields 5 Numerical Methods for Partial Differential Equations 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Journal of Non-Newtonian Fluid Mechanics 5 SIAM Journal on Mathematical Analysis 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 5 Chaos 5 European Journal of Mechanics. B. Fluids 5 Nonlinear Analysis. Real World Applications 5 Journal of Physics A: Mathematical and Theoretical 5 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 4 Computers & Mathematics with Applications 4 Physica A 4 Theoretical Population Biology 4 Chinese Annals of Mathematics. Series B 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 SIAM Journal on Applied Mathematics 4 NoDEA. Nonlinear Differential Equations and Applications 4 Acta Mathematica Sinica. English Series 4 Analysis and Applications (Singapore) 3 International Journal for Numerical Methods in Fluids 3 Physics Reports 3 Applied Mathematics and Optimization 3 Journal of Computational and Applied Mathematics 3 Studies in Applied Mathematics 3 Stochastic Analysis and Applications 3 Journal of Scientific Computing 3 Applications of Mathematics 3 Stochastic Processes and their Applications 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Communications in Nonlinear Science and Numerical Simulation 3 Communications in Contemporary Mathematics 3 Journal of Evolution Equations 3 Journal of Statistical Mechanics: Theory and Experiment 3 The European Physical Journal B. Condensed Matter and Complex Systems 2 Acta Mechanica 2 Computers and Fluids 2 International Journal of Engineering Science 2 Mathematical Biosciences 2 Reports on Mathematical Physics 2 Reviews of Modern Physics 2 Theoretical and Mathematical Physics 2 Mathematics of Computation 2 Theoretical and Computational Fluid Dynamics 2 Chaos, Solitons and Fractals 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 The Annals of Probability 2 Journal of Applied Probability 2 Numerische Mathematik 2 Proceedings of the American Mathematical Society 2 Systems & Control Letters 2 Dynamics and Stability of Systems 2 Proceedings of the National Academy of Sciences of the United States of America 2 SIAM Review 2 Bulletin of the American Mathematical Society. New Series 2 Topological Methods in Nonlinear Analysis 2 Calculus of Variations and Partial Differential Equations 2 Electronic Journal of Probability 2 Nonlinear Dynamics 2 Journal of the European Mathematical Society (JEMS) 2 Stochastics and Dynamics 2 Communications on Pure and Applied Analysis 2 Multiscale Modeling & Simulation 2 Frontiers of Mathematics in China 2 GEM - International Journal on Geomathematics ...and 103 more Serials all top 5 Cited in 41 Fields 575 Fluid mechanics (76-XX) 494 Partial differential equations (35-XX) 126 Probability theory and stochastic processes (60-XX) 125 Dynamical systems and ergodic theory (37-XX) 90 Biology and other natural sciences (92-XX) 77 Numerical analysis (65-XX) 62 Statistical mechanics, structure of matter (82-XX) 55 Classical thermodynamics, heat transfer (80-XX) 49 Ordinary differential equations (34-XX) 32 Geophysics (86-XX) 18 Systems theory; control (93-XX) 11 Real functions (26-XX) 11 Operator theory (47-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 9 Operations research, mathematical programming (90-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 8 Mechanics of deformable solids (74-XX) 8 Quantum theory (81-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Measure and integration (28-XX) 5 Integral equations (45-XX) 4 Functional analysis (46-XX) 4 Astronomy and astrophysics (85-XX) 3 Functions of a complex variable (30-XX) 3 Integral transforms, operational calculus (44-XX) 3 Statistics (62-XX) 3 Computer science (68-XX) 2 General and overarching topics; collections (00-XX) 2 Sequences, series, summability (40-XX) 2 Approximations and expansions (41-XX) 2 Differential geometry (53-XX) 2 Mechanics of particles and systems (70-XX) 1 Nonassociative rings and algebras (17-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Optics, electromagnetic theory (78-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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