Existence and uniqueness of weak solutions to Ginzburg-Landau equation with external noise and stochastic perturbation

In this paper, the Ginzburg-Landau and fractional Ginzburg-Landau equations with external noise and stochastic perturbations are studied, and we obtain the global existence and uniqueness of weak L1-solutions. Our proof is supported by the generalized Itô formula and a careful analysis of the nonlinear transport equation. After founding the well-posedness for the nonlinear transport problem in the class of Lp (1