Compressible fluids interacting with plates -- regularity and weak-strong uniqueness

TL;DR

This paper investigates the interaction between compressible viscous fluids and plates, establishing regularity results and weak-strong uniqueness for finite energy weak solutions using relative entropy methods.

Contribution

It extends the weak-strong uniqueness principle and regularity results to a fluid-structure interaction model involving compressible fluids and plates.

Findings

Finite energy weak solutions satisfy a relative energy inequality.

Displacement of the structure has improved regularity due to fluid dissipation.

Weak-strong uniqueness holds for the coupled fluid-structure system.

Abstract

In this paper, we study a nonlinear interaction problem between compressible viscous fluids and plates. For this problem, we introduce relative entropy and relative energy inequality for the finite energy weak solutions (FEWS). First, we prove that for all FEWS, the structure displacement enjoys improved regularity by utilizing the dissipation effects of the fluid onto the structure and that all FEWS satisfy the relative energy inequality. Then, we show that all FEWS enjoy the weak-strong uniqueness property, thus extending the classical result for compressible Navier-Stokes system to this fluid-structure interaction problem.