Remarks on global approximate controllability for the 2-D Navier–Stokes system with Dirichlet boundary conditions

Sergio Guerrero; Oleg Yurievich Imanuvilov; Jean-Pierre Puel

doi:10.1016/j.crma.2006.09.023

Partial Differential Equations

Remarks on global approximate controllability for the 2-D Navier–Stokes system with Dirichlet boundary conditions
[Remarques sur la contrôlabilité globale approchée du système 2-D de Navier–Stokes avec conditions au bord de type Dirichlet]

Présenté par : Pierre-Louis Lions

Sergio Guerrero ¹ ; Oleg Yurievich Imanuvilov ² ; Jean-Pierre Puel ³

¹ Laboratoire Jacques-Louis Lions, université Pierre et Marie Curie, boîte corrier, 187, 75035 Paris cedex 05, France
² Department of Mathematics, Colorado State University, 101 Weber Building, Fort Collins, CO 80523-1874, USA
³ Laboratoire de mathématiques de Versailles, université de Versailles-St-Quentin, 45, avenue des États Unis, 78035 Versailles, France

Comptes Rendus. Mathématique, Volume 343 (2006) no. 9, pp. 573-577.

Résumé
Abstract

Cette Note concerne le système de Navier–Stokes en dimension 2. Nous montrons un résultat de contrôlabilité approchée globale à l'aide de contrôles frontière.

This Note deals with the two-dimensional Navier–Stokes system. In this context, we prove a result concerning its global approximate controllability by means of boundary controls.

Reçu le : 2006-02-06
Accepté le : 2006-09-26
Publié le : 2006-10-31

DOI : 10.1016/j.crma.2006.09.023

Affiliations des auteurs :

Sergio Guerrero ¹ ; Oleg Yurievich Imanuvilov ² ; Jean-Pierre Puel ³

¹ Laboratoire Jacques-Louis Lions, université Pierre et Marie Curie, boîte corrier, 187, 75035 Paris cedex 05, France
² Department of Mathematics, Colorado State University, 101 Weber Building, Fort Collins, CO 80523-1874, USA
³ Laboratoire de mathématiques de Versailles, université de Versailles-St-Quentin, 45, avenue des États Unis, 78035 Versailles, France

@article{CRMATH_2006__343_9_573_0,
     author = {Sergio Guerrero and Oleg Yurievich Imanuvilov and Jean-Pierre Puel},
     title = {Remarks on global approximate controllability for the {2-D} {Navier{\textendash}Stokes} system with {Dirichlet} boundary conditions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {573--577},
     publisher = {Elsevier},
     volume = {343},
     number = {9},
     year = {2006},
     doi = {10.1016/j.crma.2006.09.023},
     language = {en},
}

TY  - JOUR
AU  - Sergio Guerrero
AU  - Oleg Yurievich Imanuvilov
AU  - Jean-Pierre Puel
TI  - Remarks on global approximate controllability for the 2-D Navier–Stokes system with Dirichlet boundary conditions
JO  - Comptes Rendus. Mathématique
PY  - 2006
SP  - 573
EP  - 577
VL  - 343
IS  - 9
PB  - Elsevier
DO  - 10.1016/j.crma.2006.09.023
LA  - en
ID  - CRMATH_2006__343_9_573_0
ER  -

%0 Journal Article
%A Sergio Guerrero
%A Oleg Yurievich Imanuvilov
%A Jean-Pierre Puel
%T Remarks on global approximate controllability for the 2-D Navier–Stokes system with Dirichlet boundary conditions
%J Comptes Rendus. Mathématique
%D 2006
%P 573-577
%V 343
%N 9
%I Elsevier
%R 10.1016/j.crma.2006.09.023
%G en
%F CRMATH_2006__343_9_573_0

Sergio Guerrero; Oleg Yurievich Imanuvilov; Jean-Pierre Puel. Remarks on global approximate controllability for the 2-D Navier–Stokes system with Dirichlet boundary conditions. Comptes Rendus. Mathématique, Volume 343 (2006) no. 9, pp. 573-577. doi : 10.1016/j.crma.2006.09.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.09.023/

Bibliographie
Cité par

[1] J.-M. Coron Global asymptotic stabilization for the controllable systems without drift, Math. Control Signals Systems, Volume 5 (1992) no. 3, pp. 295-312

[2] J.-M. Coron On the controllability of the 2-D incompressible Navier–Stokes equations with the Navier slip boundary conditions, ESIAN COCV, Volume 1 (1995/96), pp. 35-75

[3] C. Fabre; G. Lebeau Régularité et unicité pour le problème de Stokes, Comm. Partial Differential Equations, Volume 27 (2002) no. 3–4, pp. 437-475

[4] E. Fernández-Cara, S. Guerrero, O. Yu. Imanuvilov, J.-P. Puel, Local exact controllability of the Navier–Stokes system, J. Math. Pures Appl. 83 (12) 1501–1542

[5] O.Yu. Imanuvilov Boundary controllability of parabolic equations, Sb. Math., Volume 186 (1995), pp. 879-900

[6] Y. Giga; H. Sohr Abstract $L^{p}$ estimates for the Cauchy problem with applications to the Navier–Stokes equations in exterior domains, J. Funct. Anal., Volume 102 (1991), pp. 72-94

[7] S. Guerrero, O. Yu. Imanuvilov, J.-P. Puel, Global approximate controllability of the 2-D Navier–Stokes equations with Dirichlet boundary conditions, Preprint, 2006

Cité par Sources :

Commentaires - Politique