Pullback Attractors for Non-Newtonian Fluids with Shear Dependent Viscosity

Nonlinear dynamical analysis for globally modified incompressible non-Newtonian fluids

“…In this paper we study the autonomous dynamics of solutions of a perturbed parabolic system with nonlinear differential operator, which is physically associated with the flow of incompressible non-Newtonian fluids, e.g. [6,13,17]. This system can also be found in the literature as Ladyzhenskaya models cf.…”

“…In [2] is shown that the global attractors associated to (LM) have finite fractal dimension, in the space of the square-integrable functions with divergence-free, for p ≥ 12/5 with n = 3, and for p ≥ 2 with n = 2, also see [6,16]. On the other hand, the study of the asymptotic behavior for the non-autonomous case is carried out in [13], where is proved the existence and regularity of families of pullback attractors associated with the weak solutions of (LM) for p ≥ 12/5 in dimension n = 3 and for p > 2 in dimension n = 2. More information on these types of results can be seen in [18,22].…”