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Zbl 1128.37019
Caraballo, T.; Łukaszewicz, G.; Real, J.
Pullback attractors for asymptotically compact non-autonomous dynamical systems. (English)
[J] Nonlinear Anal., Theory Methods Appl. 64, No. 3, A, 484-498 (2006). ISSN 0362-546X

The authors introduce the concept of pullback asymptotic compactness and prove the existence of a minimal pullback attractor under very general conditions. This property, that is pullback asymptotic compactness and the existence of a family of absorbing sets provide pullback attractors existence. Despite the fact that the authors cannot prove the uniqueness of the pullback attractor under their general assumptions, however, they are able to prove that pullback attractor is minimal. As an example of application of this theory the author consider two-dimensional Navier-Stokes model in unbounded domain.
[Messoud A. Efendiev (Berlin)]

MSC 2000:: *37C70 Attractors and repellers, topological structure
37C60 Nonautonomous smooth dynamical systems
35Q35 Other equations arising in fluid mechanics

Keywords: non-autonomous (pullback) attractors; energy method; pullback asymptotically compact non-autonomous dynamical systems; cocycle; Navier-Stokes model; unbounded domains

Cited in: Zbl 1133.35025

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