Geodesic
Théorie du contrôle
Controllability of a fluid-structure interaction system coupling the Navier–Stokes system and a damped beam equation
Buffe, Rémi1 ; Takahashi, Takéo1 
1 Université de Lorraine, CNRS, Inria, IECL, 54000 Nancy, France
Comptes Rendus. Mathématique, Tome 361 (2023) no. G9, pp. 1541-1576

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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.

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DOI : 10.5802/crmath.509
Classification : 76D05, 35Q30, 74F10, 76D55, 76D27, 93B05, 93B07, 93C10
Keywords: Null controllability, Navier–Stokes systems, Carleman estimates, fluid-structure interaction systems

Buffe, Rémi 1 ; Takahashi, Takéo 1

1 Université de Lorraine, CNRS, Inria, IECL, 54000 Nancy, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Controllability of a fluid-structure interaction system coupling the {Navier{\textendash}Stokes} system and a damped beam equation},
     journal = {Comptes Rendus. Math\'ematique},
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Buffe, Rémi; Takahashi, Takéo. Controllability of a fluid-structure interaction system coupling the Navier–Stokes system and a damped beam equation. Comptes Rendus. Mathématique, Tome 361 (2023) no. G9, pp. 1541-1576. doi: 10.5802/crmath.509

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