Uniformly Random Attractor for the Three-Dimensional Stochastic Nonautonomous Camassa-Holm Equations

Abstract

We consider the uniformly random attractor for the three-dimensional stochastic nonautonomous Camassa-Holm equations in the periodic box in this paper. We associate with the concepts of uniform attractor and random attractor and produce the concept of uniformly random attractor for a process. Then we establish the existence of the uniformly random attractor in and for the equations.