In this paper, the uniform asymptotic behavior of solutions for 2D g-Navier-Stokes equations with nonlinear dampness is studied in unbounded domain. The uniform asymptotic properties of the process family is proved with the energy equation method and the uniform attractor is obtained. Finally, the dimension of the uniform attractor is estimated in the quasi-periodical case.

In this article, the global well-posedness of weak solutions for 2D non-autonomous g-Navier-Stokes equations on some bounded domains were investigated by the Faedo-Galerkin method. Then the existence of pullback attractors for 2D g-Navier-Stokes equations with nonlinear damping and time delay was obtained using the method of pullback condition (PC).