Pullback attractors for a non-autonomous incompressible non-Newtonian fluid

This paper studies the pullback asymptotic behavior of solutions for a non-autonomous incompressible non-Newtonian fluid in two-dimensional (2D) bounded domains. We first prove the existence of pull-back attractors A(V) in space V (has H-2-regularity, see notation in Section 2) and A(H) in space H (has L-2-regularity) for the cocycle corresponding to the solutions of the fluid. Then we verify the regularity of the pullback attractors by showing A(V) = A(H), Which implies the pullback asymptotic smoothing effect of the fluid in the sense that the solutions become eventually more regular than the initial data. (c) 2007 Elsevier Inc. All rights reserved.