Energy decay and global solutions for a damped free boundary fluid-elastic structure interface model with variable coefficients in elasticity

TL;DR

This paper proves the global existence and exponential decay of solutions for a fluid-structure interaction model with a free boundary, involving Navier-Stokes and variable coefficient wave equations, under small initial data.

Contribution

It introduces a novel analysis of a free boundary fluid-elastic interface with variable coefficients, establishing global solutions and decay rates.

Findings

Global existence of solutions for small initial data

Exponential decay of solutions over time

Effective handling of variable coefficients in elasticity

Abstract

We cope with a free boundary fluid-structure interaction model. In the model, the viscous incompressible fluid interacts with elastic body via the common boundary. The motion of the fluid is governed by Navier-Stokes equations while the displacement of elastic structure is described by variable coefficient wave equations. The dissipation is placed on the common boundary between fluid and elastic body. Given small initial data, the global existence of the solutions of this system is proved and the exponential decay of solutions are obtained.