The existence of global attractors for semilinear parabolic equation in spaces

In this paper, we use the iteration technique for regularity estimates, combining with the classical existence theorem of global attractors, to derive that for any k ≥ 0 the semilinear parabolic equation possesses a global attractor in H k ( Ω ) , which attracts any bounded subset of H k ( Ω ) in the H k -norm.