No abstract

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 Dσ-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.

Considered here is the first initial boundary value problem for the 2D nonautonomous g-Navier-Stokes equations in bounded domains. We prove the existence of a pullback attractor in V g for the continuous process generated by strong solutions to the problem. We also prove the exponential growth in V g and in H 2 ( , g) for the pullback attractor, when time goes to −∞.

Abstract. Considered here is the first initial boundary value problem for the two-dimensional g-Navier-Stokes equations in bounded domains. We first study the long-time behavior of strong solutions to the problem in term of the existence of a global attractor and global stability of a unique stationary solution. Then we study the long-time finite dimensional approximation of the strong solutions.

We consider the first initial boundary value problem for the 2D non-autonomous g-Navier-Stokes equations with infinite delays. We prove the existence of a pullback D-attractor for the continuous process associated to the problem with respect to a large class of non-autonomous forcing terms.