Title: Random dynamics of two-dimensional stochastic second grade fluids,
Abstract: In this paper, we consider a stochastic model of incompressible non-Newtonian
fluids of second grade on a bounded domain of $\mathbb{R}^2$ with
multiplicative noise. We first show that the solutions to the stochastic
equations of second grade fluids generate a continuous random dynamical system.
Second, we investigate the Fréchet differentiability of the random
dynamical system. Finally, we establish the asymptotic compactness of the
random dynamical system, and the existence of random attractors for the random
dynamical system, we also obtain the upper semi-continuity of the perturbed
random attractors when the noise intensity approaches zero.