Global attractor of the Cahn–Hilliard equation in spaces

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 the Cahn–Hilliard equation u t = − Δ 2 u + Δ 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.