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

22 pages. arXiv admin note: substantial text overlap with arXiv:2104.13500