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Zbl 1073.35044
Zhao, Caidi; Li, Yongsheng
$H^{2}$-compact attractor for a non-Newtonian system in two-dimensional unbounded domains.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 56, No. 7, A, 1091-1103 (2004). ISSN 0362-546X

The authors continue their study of the long-time behavior of the bipolar viscous non-Newtonian fluid in two-dimensional infinite strip $\Omega:=\Bbb R\times[-a,a]$ started in [{\it Y. Li} and {\it C. Zhao}, Acta Anal. Funct. Appl. 4, No. 4, 343--349 (2002; Zbl 1053.35117)]. In the previous paper the existence of a global attractor for that problem in the phase space $$H:=\{u\in [L^2(\Omega)]^2,\ \operatorname {div}u=0\}$$ were established [see also {\it F. Bloom} and {\it W. Hao}, Nonlinear Anal., Theory Methods Appl. 43, No. 6, 743--766 (2001; Zbl 0989.76003)], where the analogous result were established for the external forces belonging to the appropriate weighted Sobolev spaces. The main result of the present paper is the existence of a compact global attractor in a more regular phase space $$V:=\{u\in H^2(\Omega),\ \operatorname {div}u=0,\ \ u\big\vert _{\partial\Omega}=0\}.$$
[Sergey Zelik (Berlin)]
MSC 2000:
*35B41 Attractors
35Q35 Other equations arising in fluid mechanics
37L30 Attractors and their dimensions

Keywords: asymptotical compactness; two-dimensional infinite strip

Citations: Zbl 1053.35117; Zbl 0989.76003

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