${H}^{2}$-compact attractor for a non-Newtonian system in two-dimensional unbounded domains.

*(English)*Zbl 1073.35044The authors continue their study of the long-time behavior of the bipolar viscous non-Newtonian fluid in two-dimensional infinite strip ${\Omega}:=\mathbb{R}\times [-a,a]$ started in [*Y. Li* and *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

$$H:=\{u\in {\left[{L}^{2}\left({\Omega}\right)\right]}^{2},\phantom{\rule{4pt}{0ex}}divu=0\}$$

were established [see also *F. Bloom* and *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

$$V:=\{u\in {H}^{2}\left({\Omega}\right),\phantom{\rule{4pt}{0ex}}divu=0,\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}u{|}_{\partial {\Omega}}=0\}\xb7$$

Reviewer: Sergey Zelik (Berlin)