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

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.Non UBCUnreviewedAuthor affiliation: University of BordeauxFacult