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Communication Dans Un Congrès Année : 2016

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

Jean-Michel Coron
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Frédéric Marbach
Franck Sueur

Résumé

In this note we expose a particular case of a recent result obtained in [Jean-Michel Coron, Frédéric Marbach, Franck Sueur, Small time global exact null controllability of the Navier-Stokes equation with Navier slip-with-friction boundary conditions. Preprint 2016. http://arxiv.org/abs/1612.08087] 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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Dates et versions

hal-01492722 , version 1 (27-05-2017)

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Jean-Michel Coron, Frédéric Marbach, Franck Sueur. On the controllability of the Navier-Stokes equation in spite of boundary layers. Mathematical Analysis of Viscous Incompressible Fluid, Nov 2016, Kyoto, Japan. pp.162-180. ⟨hal-01492722⟩
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