Global and exponential attractors for a class of non‐Newtonian micropolar fluids

Abstract

In this paper, we consider the long‐time behavior of weak solutions for the 2D autonomous non‐Newtonian micropolar fluids. By means of the method of ℓ‐trajectories introduced by Málek and Pražák, we first establish the existence of global attractor for solution semigroup {S(t)}t ≥ 0 associated with (1)–(3) and estimate the fractal dimension of global attractor in H × L2(Ω) is finite. Then we derive the existence of exponential attractor for solution semigroup {S(t)}t ≥ 0 associated with (1.1)‐(1.3) in H × L2(Ω).