Communications in Mathematical Sciences

Volume 9 (2011)

Number 4

Random attractor for a stochastic hydrodynamical equation in Heisenberg paramagnet on an unbounded domain

Pages: 1097 – 1111

DOI: http://dx.doi.org/10.4310/CMS.2011.v9.n4.a8

Authors

B. L. Guo (Institute of Applied Physics and Computational Mathematics, Beijing, China)

C. X. Guo (Department of Mathematics, China University of Mining and Technology, Beijing)

Y. F. Guo (Institute of Applied Physics and Computational Mathematics, Beijing, China)

D. L. Li (Department of Information and Computation of Science, Guangxi University of Technology, China)

Abstract

In this paper, the asymptotic behavior of the stochastic hydrodynamical equation in the Heisenberg paramagnet on the entire two-dimensional space is studied. The asymptotic com- pactness of the stochastic dynamical system is proved by using the uniform a priori estimates for the far-field values of the solution. The existence of a random attractor is established for the corresponding stochastic dynamical system, and the regularity of the random attractor is obtained, which implies the asymptotic smoothing effect of the equation in a probability sense.

Keywords

stochastic partial differential equations, asymptotic compactness, random attractors

2010 Mathematics Subject Classification

35Q35, 60H15

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