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arXiv · 1703.07265

On the controllability of the Navier-Stokes equation in spite of boundary layers

Jean-Michel Coron·Frédéric Marbach·Franck Sueur
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Abstract

In this proceeding we expose a particular case of a recent result obtained 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.

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Jean-Michel Coron, Frédéric Marbach, Franck Sueur. 2017-03-21. On the controllability of the Navier-Stokes equation in spite of boundary layers. https://arxiv.org/abs/1703.07265

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