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This paper is concerned with pullback dynamics of 3D Navier-Stokes equationswith variable viscosity and subject to time-dependent external forces. Our mainresult establishes the existence of finite-dimensional pullback attractors in ageneral setting involving tempered universes. We also present a sufficientcondition on the viscosity coefficients that guarantees the attractors arenontrivial. We end the paper by showing the upper semi-continuity of pullbackattractors as the non-autonomous perturbation vanishes.

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