Local null controllability of the penalized Boussinesq system with a reduced number of controls
BALC'H, Kévin Le
Institut de Mathématiques de Bordeaux [IMB]
Control And GEometry [CaGE]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Institut de Mathématiques de Bordeaux [IMB]
Control And GEometry [CaGE]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
BALC'H, Kévin Le
Institut de Mathématiques de Bordeaux [IMB]
Control And GEometry [CaGE]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Control And GEometry [CaGE]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Language
en
Article de revue
This item was published in
Mathematical Control and Related Fields. 2022, vol. 12, n° 3, p. 641
AIMS
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Carleman inequality
Controllability
Nonlinear system
Penalized Stokes system
European Project
Dynamic Control and Numerics of Partial Differential Equations
ANR Project
Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003
Origin
Hal imported