A free boundary inviscid model of flow-structure interaction

TL;DR

This paper establishes local existence and uniqueness results for a coupled inviscid fluid and elastic plate system, avoiding Taylor-Rayleigh instability, with optimal regularity conditions on initial data.

Contribution

It provides the first rigorous proof of local well-posedness for a free boundary inviscid fluid-structure interaction model with optimal regularity and stability considerations.

Findings

Proved local existence and uniqueness of solutions.

Achieved optimal regularity conditions for initial data.

Demonstrated absence of Taylor-Rayleigh instability.

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 $r\geq3$. An important feature of the existence theorem is that the Taylor-Rayleigh instability does not occur.