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

TL;DR

This paper proves local existence and uniqueness of strong solutions for a compressible fluid interacting with a damped elastic plate under Navier-slip boundary conditions, using advanced mathematical techniques.

Contribution

It is the first to establish strong solutions for this fluid-structure interaction system with Navier-slip conditions, expanding the theoretical understanding.

Findings

Established local-in-time existence and uniqueness of strong solutions.

Used a decoupling and fixed point approach within an $L^{p}-L^{q}$ framework.

Addressed a novel boundary condition setting for compressible fluid-structure interaction.

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.