On the Local Existence of Solutions to the compressible Navier–Stokes-Wave System with a Free Interface

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 \(H^{2+\epsilon }\) $H^{2+ϵ}$ and the initial structure velocity is in \(H^{1.5+\epsilon }\) $H^{1.5+ϵ}$ , where \(\epsilon \in (0,1/2)\) $ϵ\in (0,1/2)$ .