On the regularity of global attractors

Details On the regularity of global attractors On the regularity of global attractors

2009-01-23

arxiv.org/abs/0901.3607v1

Mathematics

Dynamical Systems

11 pages

Scientific paper

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 $$u_{tt}-\Delta u_t-\Delta u+\phi(u)=f$$ with critical nonlinearity is considered, whose attractor is shown to possess the optimal regularity.

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