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

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 $H^{s-1/2}$.

It is not clear if Lemma 3.3 is true or not