Existence of Random Attractor for Stochastic Fractional Long-Short Wave Equations with Periodic Boundary Condition

Abstract EN

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.