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 , when is small, i.e., the same order in time as for the heat equation.
Accepté le :
DOI : 10.1051/cocv/2016034
Mots-clés : Stokes system, null controllability, Carleman estimates, spectral inequality
@article{COCV_2016__22_4_1137_0,
author = {Chaves-Silva, Felipe W. and Lebeau, Gilles},
title = {Spectral inequality and optimal cost of controllability for the {Stokes} system},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1137--1162},
publisher = {EDP-Sciences},
volume = {22},
number = {4},
year = {2016},
doi = {10.1051/cocv/2016034},
zbl = {1357.35178},
mrnumber = {3570497},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2016034/}
}
TY - JOUR AU - Chaves-Silva, Felipe W. AU - Lebeau, Gilles TI - Spectral inequality and optimal cost of controllability for the Stokes system JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2016 SP - 1137 EP - 1162 VL - 22 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2016034/ DO - 10.1051/cocv/2016034 LA - en ID - COCV_2016__22_4_1137_0 ER -
%0 Journal Article %A Chaves-Silva, Felipe W. %A Lebeau, Gilles %T Spectral inequality and optimal cost of controllability for the Stokes system %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %P 1137-1162 %V 22 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2016034/ %R 10.1051/cocv/2016034 %G en %F COCV_2016__22_4_1137_0
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://www.numdam.org/articles/10.1051/cocv/2016034/
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