Edit Profile Doering, Charles R. Compute Distance To: Compute Author ID: doering.charles-r Published as: Doering, C.; Doering, C. R.; Doering, Charles; Doering, Charles R. Homepage: http://www.lsa.umich.edu/math/people?uniqname=doering External Links: MGP · Wikidata Documents Indexed: 100 Publications since 1987, including 1 Book all top 5 Co-Authors 4 single-authored 16 Gibbon, John D. 7 Constantin, Peter 6 Thiffeault, Jean-Luc 5 Eckhardt, Bruno 4 Chini, Gregory P. 4 Lin, Zhi 4 Schumacher, Jörg 4 Worthing, Rodney A. 3 Goluskin, David 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 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 2 Wen, Baole 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 Müller, Carl E. 1 Newton, Paul K. 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, B. 1 Ryu, Chang Su 1 Schulman, Lawrence S. 1 Simon, Thilo M. 1 Thomases, Becca 1 Toppaladoddi, Srikanth 1 Waddell, Jack N. 1 Wang, Xiaoming 1 Wells, Andrew J. ...and 8 more Co-Authors all top 5 Serials 20 Journal of Fluid Mechanics 15 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 Discrete and Continuous Dynamical Systems 1 Multiscale Modeling & Simulation 1 Quantum Information Processing 1 Communications in Mathematical Sciences 1 Cambridge Texts in Applied Mathematics all top 5 Fields 70 Fluid mechanics (76-XX) 33 Partial differential equations (35-XX) 15 Classical thermodynamics, heat transfer (80-XX) 13 Dynamical systems and ergodic theory (37-XX) 11 Probability theory and stochastic processes (60-XX) 6 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 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 Calculus of variations and optimal control; optimization (49-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 84 Publications have been cited 1,313 times in 850 Documents Cited by ▼ Year ▼ Applied analysis of the Navier-Stokes equations. Zbl 0838.76016Doering, Charles R.; Gibbon, J. D. 171 1995 Low-dimensional behaviour in the complex Ginzburg-Landau equation. Zbl 0655.58021Doering, Charles R.; Gibbon, John D.; Holm, Darryl D.; Nicolaenko, Basil 93 1988 Weak and strong solutions of the complex Ginzburg-Landau equation. Zbl 0810.35119Doering, Charles R.; Gibbon, John D.; Levermore, C. David 87 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 54 1990 Infinite Prandtl number convection. Zbl 0935.76083Constantin, Peter; Doering, Charles R. 50 1999 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. 49 2005 Energy dissipation in body-forced turbulence. Zbl 1029.76025Doering, Charles R.; Foias, Ciprian 45 2002 Optimal stirring strategies for passive scalar mixing. Zbl 1241.76361Lin, Zhi; Thiffeault, Jean-Luc; Doering, Charles R. 39 2011 Exponential decay rate of the power spectrum for solutions of the Navier-Stokes equations. Zbl 1023.76513Doering, Charles R.; Titi, Edriss S. 34 1995 Bounds on vertical heat transport for infinite-Prandtl-number Rayleigh–Bénard convection. Zbl 1122.76080Doering, Charles R.; Otto, Felix; Reznikoff, Maria G. 32 2006 Bounds on Rayleigh-Bénard convection with an imposed heat flux. Zbl 1026.76048Otero, Jesse; Wittenberg, Ralf W.; Worthing, Rodney A.; Doering, Charles R. 28 2002 On upper bounds for infinite Prandtl number convection with or without rotation. Zbl 1061.76520Doering, Charles R.; Constantin, Peter 27 2001 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. 26 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 Heat transfer in convective turbulence. Zbl 0899.35078Constantin, Peter; Doering, Charles R. 21 1996 A bound on mixing efficiency for the advection-diffusion equation. Zbl 1065.76184Thiffeault, Jean-Luc; Doering, Charles R.; Gibbon, John D. 20 2004 Wall to wall optimal transport. Zbl 1329.74253Hassanzadeh, Pedram; Chini, Gregory P.; Doering, Charles R. 19 2014 The 3D Navier-Stokes problem. Zbl 1157.76008Doering, Charles R. 19 2009 Interacting particles, the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation, and duality. Zbl 1025.60027Doering, Charles R.; Mueller, Carl; Smereka, Peter 19 2003 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 Limits on enstrophy growth for solutions of the three-dimensional Navier-Stokes equations. Zbl 1172.35055Lu, Lu; Doering, Charles R. 17 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 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. 16 2012 Failure of energy stability in Oldroyd-B fluids at arbitrarily low Reynolds numbers. Zbl 1195.76174Doering, Charles R.; Eckhardt, Bruno; Schumacher, Jörg 16 2006 Bounds for heat transport in a porous layer. Zbl 0933.76090Doering, Charles R.; Constantin, Peter 16 1998 Energy dissipation in a shear layer with suction. Zbl 1184.76140Doering, Charles R.; Spiegel, Edward A.; Worthing, Rodney A. 15 2000 On the shape and dimension of the Lorenz attractor. Zbl 0838.34070Doering, Charles R.; Gibbon, J. D. 15 1995 Mean exit times for particles driven by weakly colored noise. Zbl 0681.60052Hagan, Patrick S.; Doering, Charles R.; Levermore, C. David 14 1989 Long time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion. Zbl 1398.35164Doering, Charles R.; Wu, Jiahong; Zhao, Kun; Zheng, Xiaoming 13 2018 Energy and enstrophy dissipation in steady state 2d turbulence. Zbl 1236.76029Alexakis, Alexandros; Doering, Charles R. 13 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. 13 1993 Bounds for convection between rough boundaries. Zbl 06756686Goluskin, David; Doering, Charles R. 12 2016 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. 12 2013 Rigid bounds on heat transport by a fluid between slippery boundaries. Zbl 1275.76192Whitehead, Jared P.; Doering, Charles R. 11 2012 On travelling waves for the stochastic Fisher-Kolmogorov-Petrovsky-Piscunov equation. Zbl 1095.82008Conlon, Joseph G.; Doering, Charles R. 11 2005 Variational bounds in dissipative systems. Zbl 0900.35049Constantin, Peter; Doering, Charles 11 1995 Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field. Zbl 1328.76075Gallet, Basile; Doering, Charles R. 10 2015 Symmetric factorization of the conformation tensor in viscoelastic fluid models. Zbl 1359.76023Balci, Nusret; Thomases, Becca; Renardy, Michael; Doering, Charles R. 10 2011 Extreme vorticity growth in Navier-Stokes turbulence. Zbl 1235.76030Schumacher, Jörg; Eckhardt, Bruno; Doering, Charles R. 10 2010 Internal heating driven convection at infinite Prandtl number. Zbl 1272.76230Whitehead, Jared P.; Doering, Charles R. 9 2011 A numerical method for some stochastic differential equations with multiplicative noise. Zbl 1194.65024Doering, Charles R.; Sargsyan, Khachik V.; Smereka, Peter 9 2005 Energy dissipation in body-forced plane shear flow. Zbl 1051.76028Doering, C. R.; Eckhardt, B.; Schumacher, J. 9 2003 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. 9 2002 The distribution of exit times for weakly colored noise. Zbl 0714.60072Hagan, Patrick S.; Doering, Charles R.; Levermore, C. David 9 1989 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. 8 2012 Note on the Constantin-Foias-Temam attractor dimension estimate for two- dimensional turbulence. Zbl 0728.76030Doering, Charles R.; Gibbon, John D. 8 1991 Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems. Zbl 1383.37001Tobasco, Ian; Goluskin, David; Doering, Charles R. 7 2018 Intermittency and regularity issues in \(3D\) Navier-Stokes turbulence. Zbl 1129.76014Gibbon, J. D.; Doering, Charles R. 7 2005 Bounds on convection driven by internal heating. Zbl 1071.76027Lu, Lu; Doering, Charles R.; Busse, Friedrich H. 7 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. 7 1987 Transport bounds for a truncated model of Rayleigh-Bénard convection. Zbl 1364.76056Souza, Andre N.; Doering, Charles R. 6 2015 A fast explicit operator splitting method for passive scalar advection. Zbl 1203.76126Chertock, Alina; Doering, Charles R.; Kashdan, Eugene; Kurganov, Alexander 6 2010 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. 5 2015 Energy dissipation in fractal-forced flow. Zbl 1144.81330Cheskidov, Alexey; Doering, Charles R.; Petrov, Nikola P. 5 2007 Macrophage response to Mycobacterium tuberculosis infection. Zbl 1058.92026Gammack, D.; Doering, C. R.; Kirschner, D. E. 5 2004 Attractor dimension estimates for two-dimensional shear flows. Zbl 0956.76017Doering, Charles R.; Wang, Xiaoming 5 1998 Rigorous estimates of small scales in turbulent flows. Zbl 0862.35083Constantin, Peter; Doering, Charles R.; Titi, Edriss S. 5 1996 Bounds on surface stress-driven shear flow. Zbl 1302.76050Hagstrom, George I.; Doering, Charles R. 4 2014 Variations on Kolmogorov flow: turbulent energy dissipation and mean flow profiles. Zbl 1225.76151Rollin, B.; Dubief, Y.; Doering, C. R. 4 2011 Demographic stochasticity versus spatial variation in the competition between fast and slow dispersers. Zbl 1403.92273Waddell, Jack N.; Sander, Leonard M.; Doering, Charles R. 4 2010 Intermittency in solutions of the three-dimensional Navier-Stokes equations. Zbl 1034.76013Gibbon, J. D.; Doering, Charles R. 4 2003 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 3 2006 Constructive role of noise: Fast fluctuation asymptotics of transport in stochastic ratchets. Zbl 0988.70018Doering, Charles R.; Dontcheva, Lubomira A.; Klosek, Malgorzata M. 3 1998 Ladder theorems for the \(2D\) and \(3D\) Navier-Stokes equations on a finite periodic domain. Zbl 0736.35084Bartuccelli, M.; Doering, C.; Gibbon, J. D. 3 1991 Finite dimensionality in the complex Ginzburg-Landau equation. Zbl 0741.35079Doering, C. R.; Gibbon, J. D.; Holm, D. D.; Nicolaenko, B. 3 1989 On the optimal design of wall-to-wall heat transport. Zbl 1434.76036Doering, Charles R.; Tobasco, Ian 2 2019 Diffusion-limited mixing by incompressible flows. Zbl 1390.76840Miles, Christopher J.; Doering, Charles R. 2 2018 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. 2 2015 Noise-induced statistically stable oscillations in a deterministically divergent nonlinear dynamical system. Zbl 1274.60177Boďová, Katarína; Doering, Charles 2 2012 Low-dimensional models from upper bound theory. Zbl 1372.37121Chini, Gregory P.; Dianati, Navid; Zhang, Zhexuan; Doering, Charles R. 2 2011 Models & measures of mixing & effective diffusion. Zbl 1387.76038Lin, Zhi; Bod’ová, Katarína; Doering, Charles R. 2 2010 Linear decay in multilevel quantum systems. Zbl 0729.35110Schulman, L. S.; Doering, C. R.; Gaveau, B. 2 1991 Thermal forcing and ‘classical’ and ‘ultimate’ regimes of Rayleigh-Bénard convection. Zbl 1415.76309Doering, Charles R. 1 2019 Maximum palinstrophy amplification in the two-dimensional Navier-Stokes equations. Zbl 1419.76127Ayala, Diego; Doering, Charles R.; Simon, Thilo M. 1 2018 Optimal heat transfer and optimal exit times. Zbl 1387.76096Marcotte, Florence; Doering, Charles R.; Thiffeault, Jean-Luc; Young, William R. 1 2018 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 The mixing efficiency of open flows. Zbl 1372.76058Thiffeault, Jean-Luc; Doering, Charles R. 1 2011 Rayleigh-Bénard convection with imposed heat flux. Zbl 1163.37340Johnston, Hans; Doering, Charles R. 1 2007 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 dynamics of organized structures in the axisymmetric jet mixing layer. Zbl 0728.76056Glauser, Mark; Zheng, Xiaowei; Doering, Charles R. 1 1991 On the optimal design of wall-to-wall heat transport. Zbl 1434.76036Doering, Charles R.; Tobasco, Ian 2 2019 Thermal forcing and ‘classical’ and ‘ultimate’ regimes of Rayleigh-Bénard convection. Zbl 1415.76309Doering, Charles R. 1 2019 Long time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion. Zbl 1398.35164Doering, Charles R.; Wu, Jiahong; Zhao, Kun; Zheng, Xiaoming 13 2018 Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems. Zbl 1383.37001Tobasco, Ian; Goluskin, David; Doering, Charles R. 7 2018 Diffusion-limited mixing by incompressible flows. Zbl 1390.76840Miles, 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 Optimal heat transfer and optimal exit times. Zbl 1387.76096Marcotte, Florence; Doering, Charles R.; Thiffeault, Jean-Luc; Young, William R. 1 2018 Bounds for convection between rough boundaries. Zbl 06756686Goluskin, David; Doering, Charles R. 12 2016 Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field. Zbl 1328.76075Gallet, Basile; Doering, Charles R. 10 2015 Transport bounds for a truncated model of Rayleigh-Bénard convection. Zbl 1364.76056Souza, Andre N.; Doering, Charles R. 6 2015 Maximal transport in the Lorenz equations. Zbl 1342.80005Souza, Andre N.; Doering, Charles R. 5 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. 2 2015 Wall to wall optimal transport. Zbl 1329.74253Hassanzadeh, Pedram; Chini, Gregory P.; Doering, Charles R. 19 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. 12 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. 16 2012 Rigid bounds on heat transport by a fluid between slippery boundaries. Zbl 1275.76192Whitehead, Jared P.; Doering, Charles R. 11 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. 8 2012 Noise-induced statistically stable oscillations in a deterministically divergent nonlinear dynamical system. Zbl 1274.60177Boďová, Katarína; Doering, Charles 2 2012 Optimal stirring strategies for passive scalar mixing. Zbl 1241.76361Lin, Zhi; Thiffeault, Jean-Luc; Doering, Charles R. 39 2011 Symmetric factorization of the conformation tensor in viscoelastic fluid models. Zbl 1359.76023Balci, Nusret; Thomases, Becca; Renardy, Michael; Doering, Charles R. 10 2011 Internal heating driven convection at infinite Prandtl number. Zbl 1272.76230Whitehead, Jared P.; Doering, Charles R. 9 2011 Variations on Kolmogorov flow: turbulent energy dissipation and mean flow profiles. Zbl 1225.76151Rollin, B.; Dubief, Y.; Doering, C. R. 4 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. 10 2010 A fast explicit operator splitting method for passive scalar advection. Zbl 1203.76126Chertock, Alina; Doering, Charles R.; Kashdan, Eugene; Kurganov, Alexander 6 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. 4 2010 Models & measures of mixing & effective diffusion. Zbl 1387.76038Lin, Zhi; Bod’ová, Katarína; Doering, Charles R. 2 2010 The 3D Navier-Stokes problem. Zbl 1157.76008Doering, Charles R. 19 2009 Limits on enstrophy growth for solutions of the three-dimensional Navier-Stokes equations. Zbl 1172.35055Lu, Lu; Doering, Charles R. 17 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. 5 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. 32 2006 Failure of energy stability in Oldroyd-B fluids at arbitrarily low Reynolds numbers. Zbl 1195.76174Doering, Charles R.; Eckhardt, Bruno; Schumacher, Jörg 16 2006 Energy and enstrophy dissipation in steady state 2d turbulence. Zbl 1236.76029Alexakis, Alexandros; Doering, Charles R. 13 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 3 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. 49 2005 On travelling waves for the stochastic Fisher-Kolmogorov-Petrovsky-Piscunov equation. Zbl 1095.82008Conlon, Joseph G.; Doering, Charles R. 11 2005 A numerical method for some stochastic differential equations with multiplicative noise. Zbl 1194.65024Doering, Charles R.; Sargsyan, Khachik V.; Smereka, Peter 9 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. 26 2004 A bound on mixing efficiency for the advection-diffusion equation. Zbl 1065.76184Thiffeault, Jean-Luc; Doering, Charles R.; Gibbon, John D. 20 2004 Bounds on convection driven by internal heating. Zbl 1071.76027Lu, Lu; Doering, Charles R.; Busse, Friedrich H. 7 2004 Macrophage response to Mycobacterium tuberculosis infection. Zbl 1058.92026Gammack, D.; Doering, C. R.; Kirschner, D. E. 5 2004 Interacting particles, the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation, and duality. Zbl 1025.60027Doering, Charles R.; Mueller, Carl; Smereka, Peter 19 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 45 2002 Bounds on Rayleigh-Bénard convection with an imposed heat flux. Zbl 1026.76048Otero, Jesse; Wittenberg, Ralf W.; Worthing, Rodney A.; Doering, Charles R. 28 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. 9 2002 On upper bounds for infinite Prandtl number convection with or without rotation. Zbl 1061.76520Doering, Charles R.; Constantin, Peter 27 2001 Energy dissipation in a shear layer with suction. Zbl 1184.76140Doering, Charles R.; Spiegel, Edward A.; Worthing, Rodney A. 15 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. 50 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 16 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. 3 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. 21 1996 Rigorous estimates of small scales in turbulent flows. Zbl 0862.35083Constantin, Peter; Doering, Charles R.; Titi, Edriss S. 5 1996 Applied analysis of the Navier-Stokes equations. Zbl 0838.76016Doering, Charles R.; Gibbon, J. D. 171 1995 Exponential decay rate of the power spectrum for solutions of the Navier-Stokes equations. Zbl 1023.76513Doering, Charles R.; Titi, Edriss S. 34 1995 On the shape and dimension of the Lorenz attractor. Zbl 0838.34070Doering, Charles R.; Gibbon, J. D. 15 1995 Variational bounds in dissipative systems. Zbl 0900.35049Constantin, Peter; Doering, Charles 11 1995 Weak and strong solutions of the complex Ginzburg-Landau equation. Zbl 0810.35119Doering, Charles R.; Gibbon, John D.; Levermore, C. David 87 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. 13 1993 Note on the Constantin-Foias-Temam attractor dimension estimate for two- dimensional turbulence. Zbl 0728.76030Doering, Charles R.; Gibbon, John D. 8 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. 3 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 54 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 9 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 93 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. 7 1987 all cited Publications top 5 cited Publications all top 5 Cited by 1,234 Authors 46 Doering, Charles R. 25 Wu, Jiahong 22 Titi, Edriss Saleh 19 Gibbon, John D. 18 Guo, Boling 17 Wang, Xiaoming 15 Jolly, Michael S. 13 Foiaş, Ciprian Ilie 9 Bartuccelli, Michele V. 9 Layton, William J. 9 Robinson, James Cooper 8 Chini, Gregory P. 8 Constantin, Peter 8 Dascaliuc, Radu 8 Gao, Hongjun 7 Hu, Weiwei 7 Thiffeault, Jean-Luc 7 Whitehead, Jared P. 6 Alexakis, Alexandros 6 Duan, Jinqiao 6 Fantuzzi, Giovanni 6 Kerswell, Richard Rodney 6 Levermore, C. David 6 Lu, Shujuan 6 Łukaszewicz, Grzegorz 6 Oliver, Marcel 6 Protas, Bartosz 6 Schumacher, Jörg 6 Temam, Roger Meyer 5 Biswas, Animikh 5 Boritchev, Alexandre 5 Bu, Charles 5 Fang, Tao 5 Gallet, Basile 5 Glatt-Holtz, Nathan E. 5 Goluskin, David 5 Grujić, Zoran 5 Leonov, Gennadiĭ Alekseevich 5 Lunasin, Evelyn M. 5 Mazzucato, Anna L. 5 Morgulis, Andrey Borisovich 5 Ohkitani, Koji 5 Otto, Felix 5 Park, Jungho 5 Seis, Christian 5 Shu, Ji 5 Sun, Ji Tao 5 Wen, Baole 5 Xu, Xiaojing 5 Young, William R. 4 Alarcón, Tomás 4 Ayala, Diego 4 Clancy, Damian 4 Coti Zelati, Michele 4 Crippa, Gianluca 4 Doelman, Arjen 4 Forgoston, Eric 4 Gupta, Anupam 4 Il’in, Konstantin I. 4 Kalita, Piotr 4 Kerr, Robert M. 4 Kukavica, Igor 4 Lohse, Detlef 4 Lu, Hong 4 Martinez, Vincent R. 4 Olson, Eric J. 4 Prudhomme, Serge 4 Renardy, Michael 4 Shishkina, Ol’ga Andreevna 4 Verzicco, Roberto 4 Wang, Baoxiang 4 Wang, Bixiang 4 Ye, Zhuan 4 Zaki, Tamer A. 3 Balasuriya, Sanjeeva 3 Balci, Nusret 3 Bedrossian, Jacob 3 Camassa, Roberto 3 Cao, Chongsheng 3 Chen, Shuhong 3 Chernyshenko, Sergei I. 3 Chillà, F. 3 Chow, Shui-Nee 3 Cortelezzi, Luca 3 Derrida, Bernard 3 Donzis, Diego A. 3 Dresden, Max 3 Froyland, Gary 3 Gayme, Dennice F. 3 Guermond, Jean-Luc 3 Guerrero, Pilar 3 Hagan, Patrick S. 3 Hewitt, Duncan R. 3 Hoang, Luan Thach 3 Huang, Jianhua 3 Huang, Zhehao 3 Jang, Juhi 3 Ji, Ruihong 3 Jovanović, Mihailo R. 3 Kim, Hyejin ...and 1,134 more Authors all top 5 Cited in 185 Serials 130 Journal of Fluid Mechanics 69 Physica D 36 Journal of Mathematical Physics 31 Physics of Fluids 30 Journal of Statistical Physics 29 Journal of Mathematical Analysis and Applications 28 Journal of Differential Equations 18 Physics Letters. A 16 Communications in Mathematical Physics 15 Journal of Computational Physics 15 Journal of Nonlinear Science 14 Archive for Rational Mechanics and Analysis 14 Journal of Theoretical Biology 13 Applied Mathematics and Computation 11 Journal of Mathematical Biology 10 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Applied Mathematics Letters 7 Mathematical Methods in the Applied Sciences 7 Bulletin of Mathematical Biology 7 Communications in Partial Differential Equations 7 Discrete and Continuous Dynamical Systems. Series B 6 Communications on Pure and Applied Mathematics 6 Numerical Functional Analysis and Optimization 6 Discrete and Continuous Dynamical Systems 5 Applicable Analysis 5 Journal of Functional Analysis 5 Applied Mathematics and Mechanics. (English Edition) 5 Numerical Methods for Partial Differential Equations 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Journal of Non-Newtonian Fluid Mechanics 5 Journal of Dynamics and Differential Equations 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 5 Chaos 5 Journal of Mathematical Fluid Mechanics 5 European Journal of Mechanics. B. Fluids 5 Nonlinear Analysis. Real World Applications 5 SIAM Journal on Applied Dynamical Systems 5 Journal of Statistical Mechanics: Theory and Experiment 5 Journal of Physics A: Mathematical and Theoretical 4 Computers & Mathematics with Applications 4 Nonlinearity 4 Physica A 4 Theoretical Population Biology 4 Chinese Annals of Mathematics. Series B 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Acta Mathematicae Applicatae Sinica. English Series 4 Probability Theory and Related Fields 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 SIAM Journal on Applied Mathematics 4 Acta Mathematica Sinica. English Series 4 Analysis and Applications (Singapore) 3 Computer Methods in Applied Mechanics and Engineering 3 International Journal for Numerical Methods in Fluids 3 Physics Reports 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 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 NoDEA. Nonlinear Differential Equations and Applications 3 Communications in Contemporary Mathematics 3 The European Physical Journal B. Condensed Matter and Complex Systems 3 Nonlinear Analysis. Theory, Methods & Applications 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 Applied Mathematics and Optimization 2 Numerische Mathematik 2 Proceedings of the American Mathematical Society 2 Systems & Control Letters 2 Mathematical and Computer Modelling 2 Dynamics and Stability of Systems 2 SIAM Journal on Mathematical Analysis 2 SIAM Review 2 Topological Methods in Nonlinear Analysis 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Nonlinear Dynamics 2 Communications in Nonlinear Science and Numerical Simulation 2 Journal of Evolution Equations 2 Frontiers of Mathematics in China 2 GEM - International Journal on Geomathematics 2 Evolution Equations and Control Theory 1 International Journal of Modern Physics B 1 Acta Mechanica 1 Computers and Fluids 1 International Journal of Mathematical Education in Science and Technology 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal d’Analyse Mathématique 1 Journal of Engineering Mathematics 1 Lithuanian Mathematical Journal 1 Rocky Mountain Journal of Mathematics 1 Ukrainian Mathematical Journal ...and 85 more Serials all top 5 Cited in 41 Fields 487 Fluid mechanics (76-XX) 428 Partial differential equations (35-XX) 117 Dynamical systems and ergodic theory (37-XX) 107 Probability theory and stochastic processes (60-XX) 79 Biology and other natural sciences (92-XX) 69 Numerical analysis (65-XX) 61 Statistical mechanics, structure of matter (82-XX) 49 Ordinary differential equations (34-XX) 45 Classical thermodynamics, heat transfer (80-XX) 25 Geophysics (86-XX) 13 Systems theory; control (93-XX) 9 Operator theory (47-XX) 9 Quantum theory (81-XX) 8 Real functions (26-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 7 Global analysis, analysis on manifolds (58-XX) 7 Mechanics of deformable solids (74-XX) 6 Operations research, mathematical programming (90-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Integral equations (45-XX) 4 Functional analysis (46-XX) 3 Measure and integration (28-XX) 3 Functions of a complex variable (30-XX) 3 Integral transforms, operational calculus (44-XX) 3 Statistics (62-XX) 3 Astronomy and astrophysics (85-XX) 2 Sequences, series, summability (40-XX) 2 Differential geometry (53-XX) 2 Computer science (68-XX) 2 Mechanics of particles and systems (70-XX) 1 General and overarching topics; collections (00-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 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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