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Zbl 1028.37047
Ma, Qingfeng; Wang, Shouhong; Zhong, Chengkui
Necessary and sufficient conditions for the existence of global attractors for semigroups and applications. (English)
[J] Indiana Univ. Math. J. 51, No.6, 1541-1559 (2002). ISSN 0022-2518

Summary: First we establish some necessary and sufficient conditions for the existence of the global attractor of an infinite-dimensional dynamical system, using the measure of noncompactness. Then we give a new method/recipe for proving the existence of the global attractor. The main advantage of this new method/recipe is that one needs only to verify a necessary compactness condition with the same type of energy estimates as those for establishing the absorbing set. In other words, one does not need to obtain estimates in function spaces of higher regularity. In particular, this property is useful when higher regularity is not available, as demonstrated in the example on the Navier-Stokes equations on nonsmooth domains.

MSC 2000:: *37L30 Attractors and their dimensions
35Q30 Stokes and Navier-Stokes equations
76D05 Navier-Stokes equations (fluid dynamics)

Keywords: global attractor; infinite-dimensional dynamical system; compactness condition; Navier-Stokes equations

Cited in: Zbl 1221.35203 Zbl 1174.35014 Zbl 1154.35320 Zbl 1155.37326 Zbl 1150.35340 Zbl 1144.35469 Zbl 1091.37023

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