Global attractor of a modified Swift–Hohenberg equation in Hk spaces☆

Abstract In this paper, by using an iteration procedure, regularity estimates for the linear semigroups and a classical existence theorem of global attractor, we prove that a modified Swift–Hohenberg equation u t = − Δ 2 u + g ( u ) possesses a global attractor in Sobolev space H k for all k ≥ 0 , which attracts any bounded subset of H k ( Ω ) in the H k -norm.