Abstract: The existence of the pullback attractor for the 2D non-autonomous g-Navier-Stokes 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.

Key words: pullback attractor, g-Navier-Stokes equation, pullback asymptotic compactness, pullback condition, bounded domain