Energy decay and global smooth solutions for a free boundary fluid-nonlinear elastic structure interface model with boundary dissipation

TL;DR

This paper proves the global existence and exponential decay of smooth solutions for a fluid-structure interaction model with boundary dissipation, involving Navier-Stokes fluid and nonlinear elastic boundary dynamics.

Contribution

It introduces a novel analysis of a free boundary fluid-structure model with boundary dissipation, establishing global smooth solutions and energy decay for small initial data.

Findings

Global existence of smooth solutions for small initial data

Exponential decay of the system's energy

Effective boundary dissipation mechanism

Abstract

We consider a nonlinear, free boundary fluid-structure interaction model in a bounded domain. The viscous incompressible fluid interacts with a nonlinear elastic body on the common boundary via the velocity and stress matching conditions. The motion of the fluid is governed by incompressible Navier-Stokes equations while the displacement of elastic structure is determined by a nonlinear elastodynamic system with boundary dissipation. The boundary dissipation is inserted in the velocity matching condition. We prove the global existence of the smooth solutions for small initial data and obtain the exponential decay of the energy of this system as well.