Controllability of a simplified fluid-structure interaction system
Abstract
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.
Cite
@article{arxiv.2109.00490,
title = {Controllability of a simplified fluid-structure interaction system},
author = {Rémi Buffe and Takéo Takahashi},
journal= {arXiv preprint arXiv:2109.00490},
year = {2021}
}