Local well-posedness of the equations governing the motion of a fluid-filled elastic solid

TL;DR

This paper proves the local well-posedness of a fluid-structure interaction model involving a viscous incompressible fluid and an elastic solid, establishing existence and uniqueness of solutions under certain initial conditions.

Contribution

It establishes the first rigorous proof of local well-posedness for the coupled Navier-Stokes and elasticity equations with non-zero initial data.

Findings

Unique strong solutions exist for given initial data.

Solutions are valid for initial fluid velocity in H^{5/2}.

The model is mathematically well-posed under specified conditions.

Abstract

We consider the fluid-structure interaction problem of a viscous incompressible fluid contained in an elastic solid whose motion is not prescribed. The equations governing the motion of the solid are given by the Navier equations of linear elasticity, whereas the fluid motion is described by the Navier-Stokes equations. We prove that the governing equations admit a unique strong solution corresponding to non-zero initial data for the solid initial displacement and velocity, and for a fluid initial velocity in $H^{5/2}$.