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October  2010, 26(4): 1185-1196. doi: 10.3934/dcds.2010.26.1185

Global regularity of solutions of coupled Navier-Stokes equations and nonlinear Fokker Planck equations

Peter Constantin 1, and  Gregory Seregin 2,

1. 

Department of Mathematics, The University of Chicago, Ry362A, 5734 S. University Ave, Chicago, IL 60637, United States
2. 

Oxford University, Mathematical Institute, 24-29 St Giles’, Oxford, OX1 3LB, United Kingdom

Received  January 2009 Revised  August 2009 Published  December 2009

We provide a proof of global regularity of solutions of coupled Navier-Stokes equations and Fokker-Planck equations, in two spatial dimensions, in the absence of boundaries. The proof yields a priori estimates for the growth of spatial gradients.
Keywords: Navier-Stokes equations, nonlinear Fokker-Planck equations, global existence..
Mathematics Subject Classification: 35K, 35Q30, 82C31, 76A0.
Citation: Peter Constantin, Gregory Seregin. Global regularity of solutions of coupled Navier-Stokes equations and nonlinear Fokker Planck equations. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1185-1196. doi: 10.3934/dcds.2010.26.1185
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