On time-periodic solutions to an interaction problem between compressible viscous fluids and viscoelastic beams

TL;DR

This paper establishes the existence of time-periodic weak solutions for a complex fluid-structure interaction system involving a compressible viscous fluid and a viscoelastic beam under periodic forces.

Contribution

It introduces a novel approach to proving the existence of time-periodic solutions in a nonlinear fluid-structure interaction model with periodic boundary conditions.

Findings

Existence of at least one time-periodic weak solution.

Solutions have bounded energy and fixed prescribed mass.

The model incorporates nonlinear interactions between fluid and viscoelastic structure.

Abstract

In this paper, we study a nonlinear fluid-structure interaction problem between a viscoelastic beam and a compressible viscous fluid. The beam is immersed in the fluid which fills a two-dimensional rectangular domain with periodic boundary conditions. Under the effect of periodic forces acting on the beam and the fluid, at least one time-periodic weak solution is constructed which has a bounded energy and a fixed prescribed mass.