Pullback dynamics of a 3D Navier-Stokes equation with nonlinear viscosity

TL;DR

This paper investigates the pullback dynamics of 3D Navier-Stokes equations with nonlinear viscosity, establishing the existence of finite-dimensional attractors and conditions for their nontriviality, along with their stability under perturbations.

Contribution

It introduces a general framework for pullback attractors in 3D Navier-Stokes equations with variable viscosity and provides conditions ensuring their nontriviality and stability.

Findings

Existence of finite-dimensional pullback attractors in variable viscosity 3D Navier-Stokes equations

A sufficient condition for attractors to be nontrivial

Upper semi-continuity of attractors under perturbations

Abstract

This paper is concerned with pullback dynamics of 3D Navier-Stokes equations with variable viscosity and subject to time-dependent external forces. Our main result establishes the existence of finite-dimensional pullback attractors in a general setting involving tempered universes. We also present a sufficient condition on the viscosity coefficients that guarantees the attractors are nontrivial. We end the paper by showing the upper semi-continuity of pullback attractors as the non-autonomous perturbation vanishes.