Controllability of a fluid-structure interaction system coupling the Navier–Stokes system and a damped beam equation

We show the local null-controllability of a fluid-structure interaction system coupling a viscous incompressible fluid with a damped beam located on a part of its boundary. The controls act on arbitrary small parts of the fluid domain and of the beam domain. In order to show the result, we first use...

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Bibliographic Details
Published inComptes rendus. Mathématique Vol. 361; no. G9; pp. 1541 - 1576
Main Authors Buffe, Rémi, Takahashi, Takéo
Format Journal Article
LanguageEnglish
Published Académie des sciences (Paris) 01.01.2023
Académie des sciences
Subjects
Analysis of PDEs
Carleman estimates
fluid-structure interaction systems
Mathematics
Navier–Stokes systems
Null controllability
Optimization and Control
Carleman estimates
Null controllability
Navier-Stokes system
fluid-structure interaction systems
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Summary:We show the local null-controllability of a fluid-structure interaction system coupling a viscous incompressible fluid with a damped beam located on a part of its boundary. The controls act on arbitrary small parts of the fluid domain and of the beam domain. In order to show the result, we first use a change of variables and a linearization to reduce the problem to the null-controllability of a Stokes-beam system in a cylindrical domain. We obtain this property by combining Carleman inequalities for the heat equation, for the damped beam equation and for the Laplace equation with high-frequency estimates. Then, the result on the nonlinear system is obtained by a fixed-point argument.
ISSN:1778-3569
1631-073X
1778-3569
DOI:10.5802/crmath.509