Stochastic fluctuations in the Gross-Pitaevskii equation

Anne De Bouard, Reika Fukuizumi

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We study from a mathematical point of view a model equation for a 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.

Original languageEnglish
Pages (from-to)2823-2844
Number of pages22
Issue number12
Publication statusPublished - 2007 Dec 1
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics


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