Interior gradient bounds for the 2D Navier-Stokes system

Igor Kukavica

doi:10.3934/dcds.2001.7.873

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2001, Volume 7, Issue 4: 873-882. Doi: 10.3934/dcds.2001.7.873

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Interior gradient bounds for the 2D Navier-Stokes system

Igor Kukavica^1,

1.
Department of Mathematics, University of Southern California, Los Angeles, CA 90089

Received: September 30, 2000

Revised: January 31, 2001

Published: September 2001

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Abstract

We consider $L^2$ bounds on the gradient of solutions of the Navier-Stokes equations on a general bounded 2D domain with Dirichlet boundary conditions. We obtain an upper bound for this norm on any compact subset of a given domain. We show that the bound is uniform on the global attractor and depends polynomially on the Grashof number.

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Mathematics Subject Classification: 35Q30, 76D05, 35K55, 35K15.

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