Remarks on local controllability for the Boussinesq system with Navier boundary condition

Cristhian Montoya

doi:10.5802/crmath.29

Équations aux dérivées partielles, Théorie des systèmes

Remarks on local controllability for the Boussinesq system with Navier boundary condition
[Remarque sur la contrôlabilité locale du système de Boussinesq avec la condition de frontière de Navier]

Cristhian Montoya ¹

¹ Universidad Técnica Federico Santa Maria, Casilla 110–V, Valparaiso, Chile

Comptes Rendus. Mathématique, Volume 358 (2020) no. 2, pp. 169-175.

Résumé
Abstract

Cette note concerne la contrôlabilité locale d’une classe particulière de trajectoires, ceci pour le système de Boussinesq avec la condition de Navier non linéaire et certains contrôles internes. En bref, la propriété de contrôlabilité exacte locale s’obtient en dimension deux en n’utilisant que le contrôle associé à l’équation de la chaleur. En revanche, deux contrôles scalaires sont nécessaires pour obtenir notre résultat dans le cas de dimension trois

This note deals with the local exact controllability to a particular class of trajectories for the Boussinesq system with nonlinear Navier–slip boundary conditions and internal controls having vanishing components. Briefly speaking, in two dimensions, the local exact controllability property is obtained using only one control in the heat equation, whereas two scalar controls are required in three dimensions.

Reçu le : 2019-06-29
Révisé le : 2019-12-12
Accepté le : 2020-02-27
Publié le : 2020-06-15

DOI : 10.5802/crmath.29

Affiliations des auteurs :

Cristhian Montoya ¹

¹ Universidad Técnica Federico Santa Maria, Casilla 110–V, Valparaiso, Chile

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Remarks on local controllability for the {Boussinesq} system with {Navier} boundary condition},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {169--175},
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     volume = {358},
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     year = {2020},
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Cristhian Montoya. Remarks on local controllability for the Boussinesq system with Navier boundary condition. Comptes Rendus. Mathématique, Volume 358 (2020) no. 2, pp. 169-175. doi : 10.5802/crmath.29. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.29/

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