Global random attractor for 3D stochastic Navier-Stokes equation with nonlinear colored noise

In this paper, we first introduce the definitions of random evolutionary system that associate with random evolutionary semigroup and the corresponding global weak or strong random attractor. Then we establish the existence result about global weak or strong random attractor and it’s properties like invariance and weak or strong tracking features. Finally, we use our established results to the 3D stochastic Navier-Stokes equation with nonlinear colored noise.