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

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

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