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Pullback attractors for asymptotically compact non-autonomous dynamical systems. (English) Zbl 1128.37019
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.

MSC:
37C70Attractors and repellers, topological structure
37C60Nonautonomous smooth dynamical systems
35Q35PDEs in connection with fluid mechanics