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

Abstract : 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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Contributeur : Franck Sueur <>
Soumis le : samedi 27 mai 2017 - 12:00:58
Dernière modification le : vendredi 31 août 2018 - 09:06:03
Document(s) archivé(s) le : lundi 28 août 2017 - 16:04:13


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  • HAL Id : hal-01492722, version 1
  • ARXIV : 1703.07265



Jean-Michel Coron, Frédéric Marbach, Franck Sueur. On the controllability of the Navier-Stokes equation in spite of boundary layers. 2017. 〈hal-01492722〉



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