Dynamics of Partial Differential Equations
Volume 12 (2015)
Pullback dynamical behaviors of the non-autonomous micropolar fluid flows
Pages: 265 – 288
The purpose of this work is to investigate the pullback asymptotic behaviors of solutions for non-autonomous micropolar fluid flows in two-dimensional 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 $H^2$-boundedness of the pullback attractors.
pullback attractor, tempered behavior, $H^2$-boundedness, enstrophy equality, Galerkin approximate solutions
2010 Mathematics Subject Classification
Primary 35B40. Secondary 35B41, 35Q30.