We study from a mathematical point of view a model equation for Bose Einstein condensation, in the case where the trapping potential varies randomly in time. The model is a nonlinear Schrödinger equation, with a quadratic potential with white noise fluctuations in time. We prove the existence of strong solutions in 1D and 2D in the energy space. The blow-up phenomenon will also be discussed under critical and super critical nonlinear interactions in the attractive case. This is a joint work with Reika Fukuizumi. Anne de BOUARD. Université Paris 11. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1182789924489 (pdf) Bande son disponible au format mp3 Durée : 49 mn