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In this paper we consider a Stokes system with Navier-slip boundary conditions. The main results concern the behaviour of the cost of null controllability with respect to the diffusion coefficient when the control acts in the interior. In particular, we prove in the square that for a sufficiently large time the cost decays exponentially as the diffusion coefficient vanishes, whereas in the cube we prove that for most of the control domains and for any time T > 0 the cost explodes exponentially as the diffusion coefficient vanishes.

Uniform Controllability of a Stokes Problem with a Transport Term in the Zero-Diffusion Limit