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 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.
Keywords: Null controllability, Navier-Stokes systems, Carleman estimates
@article{COCV_2022__28_1_A63_0,
author = {Buffe, R\'emi and Takahashi, Tak\'eo},
title = {Controllability of a {Stokes} system with a diffusive boundary condition},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2022},
publisher = {EDP-Sciences},
volume = {28},
doi = {10.1051/cocv/2022057},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2022057/}
}
TY - JOUR AU - Buffe, Rémi AU - Takahashi, Takéo TI - Controllability of a Stokes system with a diffusive boundary condition JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2022 VL - 28 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2022057/ DO - 10.1051/cocv/2022057 LA - en ID - COCV_2022__28_1_A63_0 ER -
%0 Journal Article %A Buffe, Rémi %A Takahashi, Takéo %T Controllability of a Stokes system with a diffusive boundary condition %J ESAIM: Control, Optimisation and Calculus of Variations %D 2022 %V 28 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2022057/ %R 10.1051/cocv/2022057 %G en %F COCV_2022__28_1_A63_0
Buffe, Rémi; Takahashi, Takéo. Controllability of a Stokes system with a diffusive boundary condition. ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 63. doi: 10.1051/cocv/2022057
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