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Journal Articles Annales de l'Institut Henri Poincaré C, Analyse non linéaire Year : 2013

Insensitizing controls for the Navier-Stokes equations

Contrôles insensibilisant pour les équations de Navier-Stokes

Mamadou Gueye
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Abstract

In this paper, we deal with the existence of insensitizing controls for the Navier-Stokes equations in a bounded domain with Dirichlet boundary conditions. We prove that there exist controls insensitizing the L2 -norm of the observation of the solution in an open subset O of the domain, under suitable assumptions on the data. This problem is equivalent to an exact controllability result for a cascade system. First we prove a global Carleman inequality for the linearized Navier-Stokes system with right-hand side, which leads to the null controllability at any time T > 0. Then, we deduce a local null controllability result for the cascade system.
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Dates and versions

hal-00906420 , version 1 (19-11-2013)

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Mamadou Gueye. Insensitizing controls for the Navier-Stokes equations. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2013, 30, pp.825-844. ⟨10.1016/j.anihpc.2012.09.005⟩. ⟨hal-00906420⟩
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