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arXiv · 2604.00973

Maximal regularity for a compressible fluid-structure interaction system with Navier-slip boundary conditions

Kuntal Bhandari·Imene Aicha Djebour·Šárka Nečasová
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Abstract

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.

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Kuntal Bhandari, Imene Aicha Djebour, Šárka Nečasová. 2026-04-16. Maximal regularity for a compressible fluid-structure interaction system with Navier-slip boundary conditions. https://arxiv.org/abs/2604.00973

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