# American Institute of Mathematical Sciences

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

 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.
Citation: Peter Constantin, Gregory Seregin. Global regularity of solutions of coupled Navier-Stokes equations and nonlinear Fokker Planck equations. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1185-1196. doi: 10.3934/dcds.2010.26.1185
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