Abstract
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 language | English |
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| Pages (from-to) | 2823-2844 |
| Number of pages | 22 |
| Journal | Nonlinearity |
| Volume | 20 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 1 Dec 2007 |
| Externally published | Yes |