Regularity of trajectory attractor and upper semicontinuity of global attractor for a 2D non-Newtonian fluid

There are two results within this paper. The one is the regularity of trajectory attractor and the trajectory asymptotic smoothing effect of the incompressible non-Newtonian fluid on 2D bounded domains, for which the solution to each initial value could be non-unique, The other is the upper semicontinuity of global attractors of the addressed fluid when the spatial domains vary from Omega(m). to Omega = R x (-L, L), where {Omega(m)}(m=1)(infinity) is an expanding sequence of simply connected, bounded and smooth subdomains of Omega such that Omega(m) -> Omega as m -> +infinity. That is, let A and A(m) be the global attractors of the fluid corresponding to Omega and Omega(m), respectively, we establish that for any neighborhood O(A) of A, the global attractor A(m) enters O(A) if m is large enough. (C) 2009 Elsevier Inc. All rights reserved.