  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.
