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 Ωm to Ω=R×(−L,L), where is an expanding sequence of simply connected, bounded and smooth subdomains of Ω such that Ωm→Ω as m→+∞. That is, let A and Am be the global attractors of the fluid corresponding to Ω and Ωm, respectively, we establish that for any neighborhood O(A) of A, the global attractor Am enters O(A) if m is large enough.