[Sur la contrôlabilité des systèmes de Navier–Stokes et Boussinesq N-dimensionnels avec contrôles scalaires]
Dans cette Note on présente quelques résultats de contrôlabilité pour des systèmes non linéaires du type Navier–Stokes et Boussinesq. On analyse l'existence de contrôles particuliers avec un nombre petit de degrés de liberté.
In this Note we present several controllability results for nonlinear systems of the Navier–Stokes and Boussinesq kind. We discuss the existence of particular controls with a small number of degrees of freedom.
Accepté le :
Publié le :
@article{CRMATH_2005__340_4_275_0,
author = {Fern\'andez-Cara, Enrique and Guerrero, Sergio and Imanuvilov, Oleg Yurievich and Puel, Jean-Pierre},
title = {On the controllability of the {\protect\emph{N}-dimensional} {Navier{\textendash}Stokes} and {Boussinesq} systems with $ N-1$ scalar controls},
journal = {Comptes Rendus. Math\'ematique},
pages = {275--280},
publisher = {Elsevier},
volume = {340},
number = {4},
year = {2005},
doi = {10.1016/j.crma.2004.12.013},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.12.013/}
}
TY - JOUR AU - Fernández-Cara, Enrique AU - Guerrero, Sergio AU - Imanuvilov, Oleg Yurievich AU - Puel, Jean-Pierre TI - On the controllability of the N-dimensional Navier–Stokes and Boussinesq systems with $ N-1$ scalar controls JO - Comptes Rendus. Mathématique PY - 2005 SP - 275 EP - 280 VL - 340 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.12.013/ DO - 10.1016/j.crma.2004.12.013 LA - en ID - CRMATH_2005__340_4_275_0 ER -
%0 Journal Article %A Fernández-Cara, Enrique %A Guerrero, Sergio %A Imanuvilov, Oleg Yurievich %A Puel, Jean-Pierre %T On the controllability of the N-dimensional Navier–Stokes and Boussinesq systems with $ N-1$ scalar controls %J Comptes Rendus. Mathématique %D 2005 %P 275-280 %V 340 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.12.013/ %R 10.1016/j.crma.2004.12.013 %G en %F CRMATH_2005__340_4_275_0
Fernández-Cara, Enrique; Guerrero, Sergio; Imanuvilov, Oleg Yurievich; Puel, Jean-Pierre. On the controllability of the N-dimensional Navier–Stokes and Boussinesq systems with $ N-1$ scalar controls. Comptes Rendus. Mathématique, Tome 340 (2005) no. 4, pp. 275-280. doi : 10.1016/j.crma.2004.12.013. http://www.numdam.org/articles/10.1016/j.crma.2004.12.013/
[1] E. Fernández-Cara, S. Guerrero, O.Yu. Imanuvilov, J.P. Puel, Local exact controllability of the Navier–Stokes system, J. Math. Pures Appl., in press
[2] Remarks on exact controllability for the Navier–Stokes equations, ESAIM Control Optim. Calc. Var., Volume 6 (2001), pp. 39-72
[3] Global Carleman estimates for weak elliptic non homogeneous Dirichlet problem, Int. Math. Res. Notices, Volume 16 (2003), pp. 883-913
[4] Carleman Estimate for a Parabolic Equation in a Sobolev Space of Negative Order and its Applications, Lecture Notes in Pure and Appl. Math., vol. 218, Dekker, New York, 2001
[5] A generic uniqueness result for the Stokes system and its control theoretical consequences (Marcellini, P.; Talenti, G.; Visentini, E., eds.), Partial Differential Equations and Applications, Lecture Notes in Pure and Appl. Math., vol. 177, Dekker, New York, 1996, pp. 221-235
Cité par Sources :
