2024-03-29T13:41:39Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/696512022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Stochastic fluctuations in the Gross-Pitaevskii equationDe Bouard, AnneFukuizumi, ReikaNonlinear Schr¨odinger equationstochastic partial differential equationswhite noise410We 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.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69651info:doi/10.14943/83992https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69651/1/pre842.pdfHokkaido University Preprint Series in Mathematics8421252007engpublisher