Communications in Mathematical Sciences
Volume 13 (2015)
Random attractor and stationary measure for stochastic long-short wave equations
Pages: 539 – 555
Asymptotic behaviors of stochastic long-short equations driven by a random force, which is smooth enough in space and white noise in time, are mainly considered. The existence and uniqueness of solutions for stochastic long-short equations are obtained via Galerkin approximation by the stopping time and the Borel-Cantelli Lemma on the basis of a priori estimates in the sense of expectation. A global random attractor and the existence of a stationary measure are investigated by the Birkhoff ergodic theorem and the Chebyshev inequality.
stochastic long-short equations, existence and uniqueness, global random attractor, stationary measure
2010 Mathematics Subject Classification
35Q35, 60H15, 76B03