Limiting Dynamics of Smooth Attractors for Non-Autonomous g-Navier-Stokes Equations with Delays

The limiting smooth dynamics of non-autonomous retarded g-Navier-Stokes equations is studied. First, we prove the existence of backward compact pullback attractor. Second, we use the spectrum decomposition method to prove the backward pullback smooth asymptotic compactness of the solution operator, and then obtain the existence of the backward compact pullback smooth attractor. Third, the upper semicontinuity of the backward compact pullback smooth attractor as the delay time tends to zero is established. Finally, we investigate the asymptotic autonomy of the backward compact pullback smooth attractor.