Fluid structure system with boundary conditions involving the pressure

TL;DR

This paper investigates a coupled fluid-structure system with pressure boundary conditions, proving local existence and uniqueness of strong solutions without small initial data assumptions.

Contribution

It introduces a novel analysis of a fluid-structure interaction with pressure boundary conditions, establishing existence and uniqueness results for the system.

Findings

Proved local strong solutions exist and are unique.

No smallness assumptions on initial data are required.

Analyzed a coupled Navier-Stokes and beam system.

Abstract

We study a coupled fluid-structure system involving boundary conditions on the pressure. The fluid is described by the incompressible Navier--Stokes equations in a 2D rectangular type domain where the upper part of the domain is described by a damped Euler--Bernoulli beam equation. Existence and uniqueness of local strong solutions without assumptions of smallness on the initial data is proved.