RANDOM ATTRACTOR AND STATIONARY MEASURE FOR STOCHASTIC LONG-SHORT WAVE EQUATIONS

摘要

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.