Georgia Institute of Technology College of Sciences

In this talk, globally modified non-autonomous 3D Navier-Stokes equations with memory and perturbations of additive noise will be discussed. Through providing theorem on the global well-posedness of the weak and strong solutions for the specific Navier-Stokes equations, random dynamical system (continuous cocycle) is established, which is associated with the above stochastic differential equations. Moreover, theoretical results show that the established random dynamical system possesses a unique compact random attractor in the space of C_H, which is periodic under certain conditions and upper semicontinuous with respect to noise intensity parameter.