Evolution of Gaussian measures and application to the one dimensional nonlinear Schr{ö}dinger equation

Abstract: In this note, we give an overview of some results obtained in [3]. This latter work is devoted to the study of the one-dimensional nonlinear Schr{\"o}dinger equation with random initial conditions. Namely, we describe the nonlinear evolution of Gaussian measures and we deduce global well-posedness and scattering results for the corresponding nonlinear Schr{\"o}dinger equation.