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Hokkaido University Preprint Series in Mathematics >
Stochastic fluctuations in the Gross-Pitaevskii equation
| Title: | Stochastic fluctuations in the Gross-Pitaevskii equation |
| Authors: | De Bouard, Anne Browse this author | | Fukuizumi, Reika Browse this author |
| Keywords: | Nonlinear Schr¨odinger equation | | stochastic partial differential equations | | white noise |
| Issue Date: | 2007 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 842 |
| Start Page: | 1 |
| End Page: | 25 |
| 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. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69651 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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