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 ${\left[0,l\right]}^3$ 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 $D\left(A^{1/2}\right)$ and $D\left(A\right)$ for the equations.