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 ∈ H r for r ≥ 3. An important feature of the existence theorem is that the Taylor-Rayleigh instability does not occur.