A free boundary inviscid model of flow-structure interaction

TL;DR

This paper proves the local existence and uniqueness of solutions for a free boundary Euler-plate system modeling inviscid fluid-structure interaction, validating previous a priori estimates.

Contribution

It establishes the first rigorous proof of local well-posedness for the 3D inviscid fluid interacting with an evolving plate with specific regularity conditions.

Findings

Proves local existence and uniqueness of solutions.

Validates earlier a priori estimates.

Addresses free boundary fluid-structure interaction.

Abstract

We address the existence and of solutions for the Euler-plate free-boundary system modeling an interaction of a three-dimensional inviscid fluid and an evolving plate. We prove the local existence and uniqueness of solutions for initial fluid and structural velocities belonging to $H^{2.5+}$ and $H^{2+}$, respectively. The results justify earlier a~priori estimates shown by two of the authors.