No abstract

The existence of the pullback attractor for the 2D non-autonomous g-NavierStokes equations on some bounded domains is investigated under the general assumptions of pullback asymptotic compactness. A new method to prove the existence of the pullback attractor for the 2D g-Navier-Stokes equations is given.

The pullback attractors for the 2D nonautonomous g-Navier-Stokes equations with linear dampness are investigated on some unbounded domains. The existence of the pullback attractors is proved by verifying the existence of pullback D-absorbing sets with cocycle and obtaining the pullback D-asymptotic compactness. Furthermore, the estimation of the fractal dimensions for the 2D g-Navier-Stokes equations is given.