Global null controllability of stochastic semilinear complex Ginzburg-Landau equations

Abstract: In this paper, we study the null controllability of forward and backward stochastic semilinear complex Ginzburg-Landau equations with global Lipschitz nonlinear terms. For this purpose, by deriving an improved global Carleman estimates for linear systems, we obtain the controllability results for the stochastic linear systems with a $L^2$-valued source term. Based on it, together with a Banach fixed point argument, the desired null controllability of semilinear systems is derived.