Pullback attractors of nonautonomous dynamical systems

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September 2006, 16(3): 587-614. doi: 10.3934/dcds.2006.16.587

Pullback attractors of nonautonomous dynamical systems

Yejuan Wang ^1, , Chengkui Zhong ^1, and Shengfan Zhou ^2,

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

Received January 2006 Revised August 2006 Published August 2006

Abstract
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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.

Keywords: 2D Navier-Stokes system., pullback attractor, nonautonomous dynamical system.

Mathematics Subject Classification: 34B40, 35L7.

Citation: Yejuan Wang, Chengkui Zhong, Shengfan Zhou. Pullback attractors of nonautonomous dynamical systems. Discrete & Continuous Dynamical Systems - A, 2006, 16 (3) : 587-614. doi: 10.3934/dcds.2006.16.587

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