On the regularity of the global attractor for a damped Rosenau equation on R

In this paper, we consider the asymptotic behaviour of the solution for a damped Rosenau equation on R. We apply a variant of Riesz-Rellich criteria, which involves the Littlewood-Paley projection operators, to prove that the damped Rosenau equation possesses a global attractor A(s) in H-s(R) for any s >= 2. Moreover, the global attractor A(s) is contained in Hs+k/2-epsilon (R) (for all epsilon > 0, k = 1, 2), if the time-independent source term is in Hs-4+k (R) and the initial data are in H-s(R). Our results establish the regularity of the global attractor for the damped Rosenau equation in fractional order Sobolev space, which is a new ingredient in this paper.