Random attractor and stationary measure for stochastic long-short wave equations

Abstract

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.

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

“…SPDE is used to describe better complex phenomenon, for example, quantum field theory, statistical mechanics, and financial mathematics; see [10][11][12] and so on. In [13][14][15][16][17][18][19], the authors obtained the existence and uniqueness of the solution and of attractors for SPDEs.…”