On the controllability of the Navier-Stokes equation in spite of boundary layers (Mathematical Analysis of Viscous Incompressible Fluid)

Abstract

In this note we expose a particular case of a recent result obtained in [6] by the authors regarding the incompressible Navier-Stokes equations in a smooth bounded and simply connected 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.