| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 63 | |
| Number of page(s) | 29 | |
| DOI | https://doi.org/10.1051/cocv/2022057 | |
| Published online | 28 September 2022 | |
Controllability of a Stokes system with a diffusive boundary condition
Université de Lorraine, CNRS, Inria, IECL, 54000 Nancy, France
* Corresponding author: takeo.takahashi@inria.fr
Received:
22
November
2021
Accepted:
7
September
2022
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.
Mathematics Subject Classification: 76D05 / 35Q30 / 93B05 / 93B07 / 93C10
Key words: Null controllability / Navier-Stokes systems / Carleman estimates
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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