Solutions globales pour l'équation de Schrödinger cubique en dimension 3

Abstract: The purpose of this article is to construct global solutions for some super-crtical Schrodinger equations using the theory of random data introduced by N.Burq and N.Tzvetkov. We begin our study by the cubic equation in three dimension. Thanks to the lens transform, it suffices to study a local theory for the Schr\"odinger equations with harmonic potential and we can establish Bourgain type bilinear estimates for the harmonic oscillator. Then, we explain how we can generalize this result in all dimensions.