English

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

Analysis of PDEs 2026-04-20 v2

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 LpLqL^{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.

Keywords

Cite

@article{arxiv.2604.00973,
  title  = {Maximal regularity for a compressible fluid-structure interaction system with Navier-slip boundary conditions},
  author = {Kuntal Bhandari and Imene Aicha Djebour and Šárka Nečasová},
  journal= {arXiv preprint arXiv:2604.00973},
  year   = {2026}
}
R2 v1 2026-07-01T11:48:23.228Z