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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.