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

Peter Constantin; Gregory Seregin

doi:10.3934/dcds.2010.26.1185

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2010, Volume 26, Issue 4: 1185-1196. Doi: 10.3934/dcds.2010.26.1185

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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
2.
Oxford University, Mathematical Institute, 24-29 St Giles’, Oxford, OX1 3LB

Received: December 31, 2008

Revised: July 31, 2009

Published: November 2010

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Abstract

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.

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Mathematics Subject Classification: 35K, 35Q30, 82C31, 76A05.

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