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Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2022

Controllability of a Stokes system with a diffusive boundary condition

Résumé

We are interested by the controllability of a fluid-structure interaction system where the fluid is viscous and incompressible and where the structure is elastic and located on a part of the boundary of the fluid's domain. In this article, we simplify this system by considering a linearization and by replacing the wave/plate equation for the structure by a heat equation. We show that the corresponding system coupling the Stokes equations with a heat equation at its boundary is null-controllable. The proof is based on Carleman estimates and interpolation inequalities. One of the Carleman estimates corresponds to the case of Ventcel boundary conditions. This work can be seen as a first step to handle the real system where the structure is modeled by the wave or the plate equation.
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Dates et versions

hal-03331176 , version 1 (01-09-2021)

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Rémi Buffe, Takéo Takahashi. Controllability of a Stokes system with a diffusive boundary condition. ESAIM: Control, Optimisation and Calculus of Variations, 2022, ⟨10.1051/cocv/2022057⟩. ⟨hal-03331176⟩
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