Existence of Random Attractor for Stochastic Fractional Long-Short Wave Equations with Periodic Boundary Condition - Na Liu; Jie Xin (Discrete Dynamics in Nature and Society)
We consider the asymptotic behaviors of stochastic fractional long-short equations driven by a random force. Under a priori estimates in the sense of expectation, using Galerkin approximation by the stopping time and the Borel-Cantelli lemma, we prove the existence and uniqueness of solutions. Then a global random attractor and the existence of a stationary measure are obtained via the Birkhoff ergodic theorem and the Chebyshev inequality.