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

Abstract

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 Ω m to Ω = R × ( − L , L ) , where { Ω m } m = 1 ∞ is an expanding sequence of simply connected, bounded and smooth subdomains of Ω such that Ω m → Ω as m → + ∞ . That is, let A and A m be the global attractors of the fluid corresponding to Ω and Ω 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.