Interior gradient bounds for the 2D Navier-Stokes system

We consider L-2 bounds on the gradient of solutions of the Navier-Stokes eq uations 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 dom ain. We show that the bound is uniform on the global attractor and depends polynomially on the Grashof number.