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Zbl 1103.76008
Dong, Boqing; Chen, Zhimin
Global attractors of two-dimensional micropolar fluid flows in some unbounded domains. (English)
[J] Appl. Math. Comput. 182, No. 1, 610-620 (2006). ISSN 0096-3003

Summary: This paper is concerned with the existence and regularity of global attractors of micropolar fluid flows in two-dimensional unbounded domains, in which the Poincaré inequality holds. Based on an asymptotic compactness argument, a $L^{2}$ global attractor is shown to exist if the stationary external vector field is in $H^{ - 1}$. Moreover, if the external vector field is in $L^{2}$, then the $L^{2}$ global attractor becomes an $H^{1}$ global attractor.

MSC 2000:: *76A05 Non-Newtonian fluids
35Q35 Other equations arising in fluid mechanics

Keywords: asymptotic compactness; Poincaré inequality

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Zentralblatt MATH Berlin [Germany]