Exponential mixing for the randomly forced NLS equation

Abstract

This paper investigates exponential mixing of the invariant measure for randomly forced nonlinear Schrödinger equation, with damping and random noise localized in space. Our study emphasizes the crucial role of exponential asymptotic compactness and control properties in establishing the ergodic properties of random dynamical systems. This work extends the series [16, 47] on the statistical behavior of randomly forced dispersive equations.