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 nonunique. 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.

Incompressible Bipolar and Non-Newtonian Viscous Fluid Flow

“…In [ZZ1] the authors study the so-called pullback asymptotic behavior of solutions for a non-autonomous, incompressible, non-Newtonian fluid in two-dimensional bounded domains after first proving the existence of pullback attractors; they establish regularity for the pullback attractors which, in turn, implies the (pullback) asymptotic smoothing effect of the fluid in the sense that solutions become eventually more regular than the initial data. Similar results are established in [ZZL3], this time with respect to the existence and regularity of pullback attractors for a non-Newtonian fluid with delays. Finally, in [ZZL3], upper semicontinuity of the global attractor for an incompressible, non-Newtonian fluid, in the two-dimensional domain D R 1 .…”

“…Similar results are established in [ZZL3], this time with respect to the existence and regularity of pullback attractors for a non-Newtonian fluid with delays. Finally, in [ZZL3], upper semicontinuity of the global attractor for an incompressible, non-Newtonian fluid, in the two-dimensional domain D R 1 . L; L/, is proven by considering an expanding sequence f m g 1 mD1 of simply connected, bounded, smooth subdomains of such that M !…”

Dynamics of non-autonomous equations of non-Newtonian fluid on 2D unbounded domains

“…There are many works concerning the unique existence, regularity and long-term behavior of solutions to equations (2.11)-(2.14) or its associated versions (see e.g. [4,5,6,12,13,14,18,21,24,28,34,36,37,38,39,40,41,42]). …”

“…The technique of truncation function has been successfully used by some researchers, see e.g. [2,31,32,41].…”

Random attractor for the Ladyzhenskaya model with additive noise

“…(1.1)-(1.3) or its associated versions (see e.g. [3,[6][7][8][9]23,25,29,30,36,37,[42][43][44][45][46]48]). For instance, Bloom and Hao [8] proved the unique existence of solution for the initial boundary value problem associated to (1.1)-(1.3) in 2D unbounded channels.…”