On an existence theory for a fluid-beam problem encompassing possible contacts

TL;DR

This paper develops a mathematical framework to prove the existence of weak solutions for a fluid-beam interaction model, including scenarios where the elastic beam contacts the fluid cavity bottom, by using approximation techniques.

Contribution

It introduces a novel functional framework for weak solutions that handle contact scenarios in fluid-beam interactions, extending previous models to include contact cases.

Findings

Proved global existence of weak solutions even with contact

Developed a new approximation method for contact scenarios

Established a framework for future analysis of fluid-structure contact problems

Abstract

In this paper we consider a coupled system of pdes modelling the interaction between a two--dimensional incompressible viscous fluid and a one--dimensional elastic beam located on the upper part of the fluid domain boundary. We design a functional framework to define weak solutions in case of contact between the elastic beam and the bottom of the fluid cavity. We then prove that such solutions exist globally in time regardless a possible contact by approximating the beam equation by a damped beam and letting this additional viscosity vanish.