A free boundary inviscid model of flow-structure interaction

Abstract

We obtain the local existence and uniqueness for a system describing interaction of an incompressible inviscid fluid, modeled by the Euler equations, and an elastic plate, represented by the fourth-order hyperbolic PDE. We provide a priori estimates for the existence with the optimal regularity $H^r$, for $r>2.5$, on the fluid initial data and construct a unique solution of the system for initial data $u_0\in H^r$ for $r\ge 3$. An important feature of the existence theorem is that the Taylor-Rayleigh instability does not occur. This is in contrast to the free-boundary Euler problem, where the stability condition on the initial pressure needs to be imposed.