Dynamics of Partial Differential Equations

Volume 12 (2015)

Number 3

Pullback dynamical behaviors of the non-autonomous micropolar fluid flows

Pages: 265 – 288

DOI: http://dx.doi.org/10.4310/DPDE.2015.v12.n3.a4

Authors

Caidi Zhao (Department of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang, China)

Wenlong Sun (Department of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang, China)

Cheng Hsiung Hsu (Department of Mathematics, National Central University, Chung-Li, Taiwan)

Abstract

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.

Keywords

pullback attractor, tempered behavior, $H^2$-boundedness, enstrophy equality, Galerkin approximate solutions

2010 Mathematics Subject Classification

Primary 35B40. Secondary 35B41, 35Q30.

Full Text (PDF format)