$G$-mean random attractors for complex Ginzburg–Landau equations with probability-uncertain initial data

In this paper, a class of complex Ginzburg–Landau equations with random initial data is investigated, where the randomness may be of probability uncertainty. The existence and uniqueness of global solution for such system are proved under the framework of nonlinear expectation. Then, the existence of pullback G-mean random attractors for the G-mean random dynamical system generated by the solution operators of (1.1) is investigated not only in \n, but also in a weighted space \n. Moreover, such attractor is periodic if the nonautonomous deterministic forcing is time periodic.