Pullback attractors on time-dependent spaces for fluid-structure interaction systems

TL;DR

This paper investigates the long-term behavior of a coupled fluid-structure interaction system, demonstrating the existence of a pullback attractor on time-dependent spaces for the 3D Navier-Stokes and elasticity equations.

Contribution

It establishes the existence of a pullback attractor for a non-autonomous fluid-structure system on evolving spaces, advancing understanding of its asymptotic dynamics.

Findings

Existence of a pullback attractor for the coupled system

Demonstration of long-time stability of solutions

Analysis on time-dependent spaces for non-autonomous systems

Abstract

We study the long-time dynamics of a non-autonomous coupled system consisting of the 3D linearized Na\-vier--Stokes equations and nonlinear elasticity equations. We show that this problem generates a process on time-dependent spaces possessing a pullback attractor.