Pullback exponential attractors for a class of non-Newtonian micropolar fluids

Abstract

In this paper, we consider the pullback asymptotic behaviors of weak solutions for the 2D non-autonomous Non-Newtonian micropolar fluids. Employing the methods of ℓ-trajectories in [31], we first establish the existence of a finite dimensional pullback attractor and a pullback exponential attractor for the process {L(t,τ)}t≥τ associated with (1.2)-(1.4) in the phase space Xℓ. Then we construct a pullback exponential attractor for the process {U(t,τ)}t≥τ associated with (1.2)-(1.4) in the original phase space H×L2(Ω).