Pullback attractors of nonautonomous dynamical systems

Yejuan Wang; Chengkui Zhong; Shengfan Zhou

doi:10.3934/dcds.2006.16.587

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2006, Volume 16, Issue 3: 587-614. Doi: 10.3934/dcds.2006.16.587

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Pullback attractors of nonautonomous dynamical systems

1.
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000
2.
Department of Mathematics, Shanghai University, Shanghai, 200436

Received: December 31, 2005

Revised: July 31, 2006

Published: August 2006

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Abstract

We present the necessary and sufficient conditions and a new method to study the existence of pullback attractors of nonautonomous infinite dimensional dynamical systems. For illustrating our method, we apply it to nonautonomous 2D Navier-Stokes systems. We also show that the parametrically inflated pullback attractors and uniform attractors are robust with respect to the perturbations of both cocycle mappings and driving systems. As an example, we consider the nonautonomous 2D Navier-Stokes system with rapidly oscillating external force.

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Mathematics Subject Classification: 34B40, 35L70.

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