Pullback dynamical behaviors of the non-autonomous micropolar fluid flows

The purpose of this work is to investigate the pullback asymptotic behaviors of solutions for non-autonomous micropolar fluid flows in twodimensional bounded domains. On the base of the known results concerning the global well-posedness of the solutions, we apply the technique of enstrophy equality, combining with the estimates on the solutions, to prove the existence and regularity of the pullback attractors for the generated evolution process for the universe of fixed bounded sets and for another universe with a tempered condition in different phase spaces. Then we use the estimates of the solutions to analyze the tempered behavior and H²-boundedness of the pullback attractors.