[Remarques sur la contrôlabilité exacte des systèmes de Stokes et Navier–Stokes]
Cette Note concerne la contrôlabilité des systèmes de Stokes et Navier–Stokes avec contrôles distribués pour lesquels les supports sont éventuellement petits. On présente d'abord une nouvelle inégalité globale de Carleman pour les solutions d'un problème de type Stokes. On en déduit la contrôlabilité exacte à zéro en tout temps T>0. Ensuite, on présente un résultat local de contrôlabilité exacte sur les trajectoires pour le système de Navier–Stokes.
This Note deals with the controllability of Stokes and Navier–Stokes systems with distributed controls with support in possibly small subdomains. We first present a new global Carleman inequality for the solutions to Stokes-like systems that leads to the null controllability at any time T>0. Then, we present a local result concerning exact controllability to trajectories of the Navier–Stokes system.
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@article{CRMATH_2004__338_5_375_0,
author = {Fern\'andez-Cara, Enrique and Guerrero, Sergio and Imanuvilov, Oleg Yurievich and Puel, Jean-Pierre},
title = {Remarks on exact controllability for {Stokes} and {Navier{\textendash}Stokes} systems},
journal = {Comptes Rendus. Math\'ematique},
pages = {375--380},
publisher = {Elsevier},
volume = {338},
number = {5},
year = {2004},
doi = {10.1016/j.crma.2003.12.016},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2003.12.016/}
}
TY - JOUR AU - Fernández-Cara, Enrique AU - Guerrero, Sergio AU - Imanuvilov, Oleg Yurievich AU - Puel, Jean-Pierre TI - Remarks on exact controllability for Stokes and Navier–Stokes systems JO - Comptes Rendus. Mathématique PY - 2004 SP - 375 EP - 380 VL - 338 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2003.12.016/ DO - 10.1016/j.crma.2003.12.016 LA - en ID - CRMATH_2004__338_5_375_0 ER -
%0 Journal Article %A Fernández-Cara, Enrique %A Guerrero, Sergio %A Imanuvilov, Oleg Yurievich %A Puel, Jean-Pierre %T Remarks on exact controllability for Stokes and Navier–Stokes systems %J Comptes Rendus. Mathématique %D 2004 %P 375-380 %V 338 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2003.12.016/ %R 10.1016/j.crma.2003.12.016 %G en %F CRMATH_2004__338_5_375_0
Fernández-Cara, Enrique; Guerrero, Sergio; Imanuvilov, Oleg Yurievich; Puel, Jean-Pierre. Remarks on exact controllability for Stokes and Navier–Stokes systems. Comptes Rendus. Mathématique, Tome 338 (2004) no. 5, pp. 375-380. doi : 10.1016/j.crma.2003.12.016. http://www.numdam.org/articles/10.1016/j.crma.2003.12.016/
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