Existence of time-periodic strong solutions to a fluid-structure system

TL;DR

This paper proves the existence of time-periodic strong solutions for a coupled fluid-structure system modeling blood flow in arteries, using nonlinear Navier-Stokes and beam equations with periodic boundary conditions.

Contribution

It establishes the existence of time-periodic solutions for a nonlinear fluid-structure interaction model under small source term assumptions.

Findings

Existence of time-periodic strong solutions proven.

Solutions exist under smallness conditions on source terms.

Model applies to blood flow in arteries.

Abstract

We study a nonlinear coupled fluid-structure system modelling the blood flow through arteries. The fluid is described by the incompressible Navier-Stokes equations in a 2D rectangular domain where the upper part depends on a structure satisfying a damped Euler-Bernoulli beam equation. The system is driven by time-periodic source terms on the inflow and outflow boundaries. We prove the existence of time-periodic strong solutions for this problem under smallness assumptions for the source terms.