On the local existence of solutions to the fluid-structure interaction problem with a free interface

TL;DR

This paper proves the local existence of solutions for a fluid-structure interaction model involving an incompressible fluid and elastic body, under specific initial velocity regularity conditions.

Contribution

It establishes local existence results for the fluid-structure interaction problem with initial data in certain Sobolev spaces, extending previous theoretical understanding.

Findings

Proves local existence for initial velocities in H^s with s>3/2.

Demonstrates well-posedness under specified regularity conditions.

Provides mathematical foundation for fluid-elastic body interaction models.

Abstract

We address a system of equations modeling an incompressible fluid interacting with an elastic body. We prove the local existence when the initial velocity belongs to the space $H^{s}$, where $s>3/2$ and the initial structure velocity is in $H^{s-1/2}$.