Geodesic
Spectral inequality and optimal cost of controllability for the Stokes system
Chaves-Silva, Felipe W.1 ; Lebeau, Gilles1 
1 Universitéde Nice Sophia-Antipolis, Laboratoire Jean A. Dieudonné, UMR CNRS 6621, Parc Valrose, 06108 Nice cedex 02, France.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1137-1162.

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In this paper we present a new proof of the null controllability property for the Stokes system. The proof is based on a new spectral inequality for the eigenfunctions of the Stokes operator. As a consequence, we obtain the cost of the null controllability for the Stokes system of order e C/T , when T is small, i.e., the same order in time as for the heat equation.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2016034
Classification : 35K40, 35Q30, 49J20
Keywords: Stokes system, null controllability, Carleman estimates, spectral inequality

Chaves-Silva, Felipe W. 1 ; Lebeau, Gilles 1

1 Universitéde Nice Sophia-Antipolis, Laboratoire Jean A. Dieudonné, UMR CNRS 6621, Parc Valrose, 06108 Nice cedex 02, France. 
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Chaves-Silva, Felipe W.; Lebeau, Gilles. Spectral inequality and optimal cost of controllability for the Stokes system. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1137-1162. doi : 10.1051/cocv/2016034. http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016034/

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