LAUSR

This paper is concerned with pullback dynamics of a 3D Navier-Stokes equations with variable viscosity and subject to perturbations of time-dependent external forces. Under suitable assumptions on the external force, which is possibly unbounded, we establish the existence of finite-dimensional minimal pullback attractor in a general setting involving tempered universe. We also present a sufficient condition on the viscosity coefficients in order for the attractors to be non-trivial. We conclude the paper by showing the upper semi-continuity of pullback attractors as the non-autonomous perturbation vanishes.