Maximal regularity for a compressible fluid-structure interaction system with Navier-slip boundary conditions
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| Format: | Preprint |
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2026
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| _version_ | 1866908972900941824 |
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| author | Bhandari, Kuntal Djebour, Imene Aicha Nečasová, Šárka |
| author_facet | Bhandari, Kuntal Djebour, Imene Aicha Nečasová, Šárka |
| contents | We investigate a fluid-structure interaction system in which the dynamics of the fluid is described by the compressible Navier-Stokes equations, while the elastic structure is modeled by a damped plate equation. The fluid evolves in a three-dimensional bounded domain, with the structure occupies a part of its boundary. Instead of standard no-slip boundary conditions, we consider the Navier-slip boundary conditions at the fluid-structure interface as well as at the fixed boundary. We establish the local-in-time existence and uniqueness of strong solutions within $L^{p}-L^{q}$ framework. The existence result is obtained for small time by decoupling the linearized system and employing a cascade strategy combined with the Tikhonov fixed point theorem, whereas the uniqueness is shown by deriving weak regularity properties for the associated linear coupled operator in a Hilbert space setting. It is the first result addressing strong solutions for a compressible fluid interacting with a damped plate under Navier-slip boundary conditions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_00973 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximal regularity for a compressible fluid-structure interaction system with Navier-slip boundary conditions Bhandari, Kuntal Djebour, Imene Aicha Nečasová, Šárka Analysis of PDEs We investigate a fluid-structure interaction system in which the dynamics of the fluid is described by the compressible Navier-Stokes equations, while the elastic structure is modeled by a damped plate equation. The fluid evolves in a three-dimensional bounded domain, with the structure occupies a part of its boundary. Instead of standard no-slip boundary conditions, we consider the Navier-slip boundary conditions at the fluid-structure interface as well as at the fixed boundary. We establish the local-in-time existence and uniqueness of strong solutions within $L^{p}-L^{q}$ framework. The existence result is obtained for small time by decoupling the linearized system and employing a cascade strategy combined with the Tikhonov fixed point theorem, whereas the uniqueness is shown by deriving weak regularity properties for the associated linear coupled operator in a Hilbert space setting. It is the first result addressing strong solutions for a compressible fluid interacting with a damped plate under Navier-slip boundary conditions. |
| title | Maximal regularity for a compressible fluid-structure interaction system with Navier-slip boundary conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.00973 |