On the existence and the uniqueness of the solution to a fluid-structure interaction problem

TL;DR

This paper proves the existence and uniqueness of solutions for a linearized fluid-structure interaction model, providing foundational mathematical results for understanding such coupled systems.

Contribution

It establishes the first rigorous proof of existence and uniqueness for a linearized fluid-structure interaction PDE system under natural regularity conditions.

Findings

Existence of solutions is proven under specified assumptions.

Uniqueness of solutions is established for the linearized model.

Provides a mathematical foundation for further analysis of fluid-structure interactions.

Abstract

In this paper we consider the linearized version of a system of partial differential equations arising from a fluid-structure interaction model. We prove the existence and the uniqueness of the solution under natural regularity assumptions.