On the regularity of global attractors

Monica Conti; Vittorino Pata

doi:10.3934/dcds.2009.25.1209

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2009, Volume 25, Issue 4: 1209-1217. Doi: 10.3934/dcds.2009.25.1209

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On the regularity of global attractors

Monica Conti^1, and
Vittorino Pata^1,

1.
Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano

Received: December 31, 2008

Revised: May 31, 2009

Published: October 2009

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Abstract

This note is focused on a novel technique 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, we consider the semigroup generated by the strongly damped wave equation with critical nonlinearity, whose attractor is shown to possess the optimal regularity.

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Mathematics Subject Classification: Primary: 34D45, 47H20; Secondary: 35B33, 35L05.

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