Long-time behavior for 2D non-autonomous g-Navier-Stokes equations

We study the first initial boundary value problem for the 2D non-autonomous g-Navier-Stokes equations in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality. The existence of a weak solution to the problem is proved by using the Galerkin method. We then show the existence of a unique minimal finite-dimensional pullback D σ-attractor for the process associated to the problem with respect to a large class of non-autonomous forcing terms. Furthermore, when the force is time-independent and "small", the existence, uniqueness and global stability of a stationary solution are also studied. © Instytut Matematyczny PAN, 2012.