Dept. Math, Hokkaido Univ. EPrints Server

Stochastic fluctuations in the Gross-Pitaevskii equation

Preprint Series # 842
De Bouard, Anne and Fukuizumi, Reika Stochastic fluctuations in the Gross-Pitaevskii equation. (2007);

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Abstract

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.

Item Type:Preprint
Additional Information:20
Uncontrolled Keywords:Nonlinear Schr\"odinger equation, stochastic partial differential equations, white noise
Subjects:60-xx PROBABILITY THEORY AND STOCHASTIC PROCESSES
35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:1694