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Controllability of the Navier-Stokes equations with Navier slip-with-friction boundary conditions. Sueur, Franck


In this work in collaboration with J.-M. Coron and F. Marbach, we consider the incompressible Navier-Stokes equations in a smooth bounded domain, either in 2D or in 3D, with a Navier slip-with-friction boundary condition except on a part of the boundary. This under-determination encodes that one has control over the remaining part of the boundary. We prove that for any initial data, for any positive time, there exists a weak Leray solution which vanishes at this given time.

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