Global attractor of the Cahn-Hilliard equation in Hk 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 ut=−Δ2u+Δg(u) possesses a global attractor in Sobolev space Hk for all k⩾0, which attracts any bounded subset of Hk(Ω) in the Hk-norm.