On the Local Existence of Solutions to the Fluid–Structure Interaction Problem with a Free Interface

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 \(H^{1.5+\epsilon }\) $H^{1.5+ϵ}$ and the initial structure velocity is in \(H^{1+\epsilon }\) $H^{1+ϵ}$ , where \(\epsilon \in (0, 1/20)\) $ϵ\in (0,1/20)$ .