Asymptotic behaviour of the non-autonomous 3D Navier-Stokes problem with coercive force

TL;DR

This paper studies the long-term behavior of weak solutions to the 3D Navier-Stokes equations with unbounded external forces, constructing pullback attractors to understand their asymptotic dynamics.

Contribution

It introduces a method to construct pullback attractors for non-autonomous 3D Navier-Stokes equations with coercive forces that may grow unbounded over time.

Findings

Existence of pullback attractors for weak solutions

Framework for unbounded external forces in Navier-Stokes

Insights into asymptotic behavior of non-autonomous flows

Abstract

We construct pullback attractors to the weak solutions of the three-dimensional Dirichlet problem for the incompressible Navier-Stokes equations in the case when the external force may become unbounded as time goes to plus or minus infinity.