The existence of global attractors for 2D Navier-Stokes equations in H k spaces

In this paper, we prove that the 2D Navier-Stokes equations possess a global attractor in H k(., R 2) for any k . 1, which attracts any bounded set of H k(., R 2) in the H k-norm. The result is established by means of an iteration technique and regularity estimates for the linear semigroup of operator, together with a classical existence theorem of global attractor. This extends Ma, Wang and Zhong.s conclusion.