# American Institute of Mathematical Sciences

October  2001, 7(4): 873-882. doi: 10.3934/dcds.2001.7.873

## Interior gradient bounds for the 2D Navier-Stokes system

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

Received  October 2000 Revised  February 2001 Published  July 2001

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.
Citation: Igor Kukavica. Interior gradient bounds for the 2D Navier-Stokes system. Discrete & Continuous Dynamical Systems - A, 2001, 7 (4) : 873-882. doi: 10.3934/dcds.2001.7.873
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