Global attractor of a modified Swift–Hohenberg equation in HkHk 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 a modified Swift–Hohenberg equation ut=−Δ2u+g(u)ut=−Δ2u+g(u) possesses a global attractor in Sobolev space HkHk for all k≥0k≥0, which attracts any bounded subset of Hk(Ω)Hk(Ω) in the HkHk-norm.