Stochastic fluctuations in the Gross-Pitaevskii equation
Preprint Series # 842
De Bouard, Anne and Fukuizumi, Reika Stochastic fluctuations in the Gross-Pitaevskii equation. (2007);
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 the so called Gross-Pitaevskii equation, with a
quadratic potential with white noise fluctuations in time.
We prove the existence of solutions in 1D and 2D
in the energy space.
The blow-up phenomenon is also discussed
under critical and super critical nonlinear
interactions in the attractive case.