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# 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: https://dx.doi.org/10.4310/CMS.2011.v9.n4.a8

#### Authors

#### 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

Published 29 July 2011