Existence of global strong solutions to a beam-fluid interaction system

TL;DR

This paper proves the global existence of strong solutions for a fluid-structure interaction model simulating blood flow in elastic arteries, ensuring no contact occurs between the artery wall and the fluid cavity in finite time.

Contribution

It establishes the first known global-in-time strong solutions for a viscous fluid interacting with a viscoelastic structure, preventing finite-time contact.

Findings

Proved global existence of strong solutions.

Demonstrated no finite-time contact occurs.

First such result for viscous fluid-structure interaction.

Abstract

We study an unsteady non linear fluid-structure interaction problem which is a simplified model to describe blood flow through viscoleastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier-Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear viscoelastic beam equation. The fluid and the structure are fully coupled via interface conditions prescribing the continuity of the velocities at the fluid-structure interface and the action-reaction principle. We prove that strong solutions to this problem are global-in-time. We obtain in particular that contact between the viscoleastic wall and the bottom of the fluid cavity does not occur in finite time. To our knowledge, this is the first occurrence of a no-contact result, but also of existence of strong solutions globally in time, in the frame of interactions between a viscous fluid and a deformable structure.