Electron. J. Diff. Equ., Vol. 2014 (2014), No. 246, pp. 1-19.

Random attractors in H^1 for stochastic two dimensional micropolar fluid flows with spatial-valued noises

Wenqiang Zhao

This work studies the long-time behavior of two-dimensional micropolar fluid flows perturbed by the generalized time derivative of the infinite dimensional Wiener processes. Based on the omega-limit compactness argument as well as some new estimates of solutions, it is proved that the generated random dynamical system admits an H^1-random attractor which is compact in H^1 space and attracts all tempered random subsets of L^2 space in H^1 topology. We also give a general abstract result which shows that the continuity condition and absorption of the associated random dynamical system in H^1 space is not necessary for the existence of random attractor in H^1 space.

Submitted March 26, 2014. Published November 21, 2014.
Math Subject Classifications: 60H15, 35R60, 35B40, 35B41.
Key Words: Random dynamical system; stochastic micropolar fluid flows; random attractor; additive noises; Wiener process.

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Wenqiang Zhao
School Of Mathematics and Statistics
Chongqing Technology and Business University
Chongqing 400067, China
email: gshzhao@sina.com

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