On the local existence of solutions to the Navier-Stokes-wave system with a free interface

Abstract

We address a system of equations modeling a compressible fluid interacting with an elastic body in dimension three. We prove the local existence and uniqueness of a strong solution when the initial velocity belongs to the space $H^{2+\epsilon}$ and the initial structure velocity is in $H^{1.5+\epsilon}$ , where $\epsilon \in (0, 1/2)$.