On the Regularity of Global Attractors

This note is focused on a novel technique in order to establish the boundedness in more regular spaces for global attractors of dissipative dynamical systems, without appealing to uniform-in-time estimates. As an application of the abstract result, the semigroup generated by the strongly damped wave equation utt −∆ut −∆u + φ(u) = f with critical nonlinearity is considered, whose attractor is shown to possess the optimal regularity.