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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Académie des sciences
2023-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.509/ |
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| author | Buffe, Rémi Takahashi, Takéo |
| author_facet | Buffe, Rémi Takahashi, Takéo |
| author_sort | Buffe, Rémi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c014220a3956486da343e9d3ff98d15e |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-c014220a3956486da343e9d3ff98d15e2025-02-07T11:10:50ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-11-01361G91541157610.5802/crmath.50910.5802/crmath.509Controllability of a fluid-structure interaction system coupling the Navier–Stokes system and a damped beam equationBuffe, Rémi0Takahashi, Takéo1Université de Lorraine, CNRS, Inria, IECL, 54000 Nancy, FranceUniversité de Lorraine, CNRS, Inria, IECL, 54000 Nancy, FranceWe 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.509/Null controllabilityNavier–Stokes systemsCarleman estimatesfluid-structure interaction systems |
| spellingShingle | Buffe, Rémi Takahashi, Takéo Controllability of a fluid-structure interaction system coupling the Navier–Stokes system and a damped beam equation Comptes Rendus. Mathématique Null controllability Navier–Stokes systems Carleman estimates fluid-structure interaction systems |
| title | Controllability of a fluid-structure interaction system coupling the Navier–Stokes system and a damped beam equation |
| title_full | Controllability of a fluid-structure interaction system coupling the Navier–Stokes system and a damped beam equation |
| title_fullStr | Controllability of a fluid-structure interaction system coupling the Navier–Stokes system and a damped beam equation |
| title_full_unstemmed | Controllability of a fluid-structure interaction system coupling the Navier–Stokes system and a damped beam equation |
| title_short | Controllability of a fluid-structure interaction system coupling the Navier–Stokes system and a damped beam equation |
| title_sort | controllability of a fluid structure interaction system coupling the navier stokes system and a damped beam equation |
| topic | Null controllability Navier–Stokes systems Carleman estimates fluid-structure interaction systems |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.509/ |
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