Wong-Zakai approximations and attractors for stochastic three-dimensional globally modified Navier-Stokes equations driven by nonlinear noise

We analyze the asymptotic behavior of the stochastic three dimensional globally modified Navier-Stokes equations with general Lipschitz nonlinear noise. By using the Wong-Zakai approximation, we first show that the approximate equation has a unique random attractor, and then when the stochastic equation is driven by a linear multiplicative noise or additive white noise, we show the convergence of solutions and attractors of Wong-Zakai approximations of the approximate random systems as the size of the approximation tends to zero.