Communications in Mathematical Sciences
Volume 9 (2011)
Random attractor for a stochastic hydrodynamical equation in Heisenberg paramagnet on an unbounded domain
Pages: 1097 – 1111
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.
stochastic partial differential equations, asymptotic compactness, random attractors
2010 Mathematics Subject Classification