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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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https://hal.archives-ouvertes.fr/hal-01492722
Contributor : Franck Sueur <>
Submitted on : Saturday, May 27, 2017 - 12:00:58 PM
Last modification on : Monday, December 14, 2020 - 5:24:26 PM
Long-term archiving on: : Monday, August 28, 2017 - 4:04:13 PM

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

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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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