PULLBACK ATTRACTORS FOR STRONG SOLUTIONS OF 2D NON-AUTONOMOUS g-NAVIER-STOKES EQUATIONS

Considered here is the first initial boundary value problem for the 2D non-autonomous g-Navier-Stokes equations in bounded domains. We prove the existence of a pullback attractor in Vg for the continuous process generated by strong solutions to the problem. We also prove the exponential growth in Vg and in H2(Ω, g) for the pullback attractor, when time goes to −∞. © 2014, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.