Regularity of global attractor for the fourth-order reaction–diffusion equation

In this paper, it is proved that the fourth-order reaction–diffusion equation 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 by using an iteration procedure, regularity estimates for the linear semigroups and a classical existence theorem of global attractor.