BÁRCENA-PETISCO, Jon Asier; BALC'H, Kévin Le

doi:10.3934/mcrf.2021038

Métadonnées

Licence d’utilisation du document

BÁRCENA-PETISCO, Jon Asier
Universidad Autónoma de Madrid [UAM]
Fundación Deusto

BALC'H, Kévin Le
Institut de Mathématiques de Bordeaux [IMB]
Control And GEometry [CaGE]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]

Langue

Article de revue

Ce document a été publié dans

Mathematical Control and Related Fields. 2022, vol. 12, n° 3, p. 641

AIMS

Résumé en anglais

In this paper we consider the Boussinesq system with homogeneous Dirichlet boundary conditions and defined in a regular domain Ω ⊂ R^N for N = 2 and N = 3. The incompressibility condition of the fluid is replaced by its approximation by penalization with a small parameter ε > 0. We prove that our system is locally null controllable using a control with a restricted number of components, defined in an open set ω contained in Ω and whose cost is bounded uniformly when ε → 0. The proof is based on a linearization argument and the null-controllability of the linearized system is obtained by proving a new Carleman estimate for the adjoint system. This observability inequality is obtained thanks to the coercivity of some second order differential operator involving crossed derivatives.< Réduire

Mots clés en anglais

Carleman inequality

Controllability

Nonlinear system

Penalized Stokes system

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191551

DOI

http://dx.doi.org/10.3934/mcrf.2021038

Projet Européen

Dynamic Control and Numerics of Partial Differential Equations

Project ANR

Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251