Electron. J. Diff. Equ.,
Vol. 2014 (2014), No. 246, pp. 119.
Random attractors in H^1 for stochastic two dimensional micropolar
fluid flows with spatialvalued noises
Wenqiang Zhao
Abstract:
This work studies the longtime behavior of twodimensional micropolar fluid
flows perturbed by the generalized time derivative of the infinite
dimensional Wiener processes. Based on the omegalimit compactness
argument as well as some new estimates of solutions, it is proved that
the generated random dynamical system admits an H^1random 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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