Stochastic fluctuations in the GrossPitaevskii equation
Preprint Series # 842 De Bouard, Anne and Fukuizumi, Reika Stochastic fluctuations in the GrossPitaevskii equation. (2007); AbstractWe 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 GrossPitaevskii 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 blowup phenomenon is also discussed
under critical and super critical nonlinear
interactions in the attractive case.
