Carles, R. Remarks on nonlinear Schrödinger equations with harmonic potential. (English) Zbl 1021.81013 Ann. Henri Poincaré 3, No. 4, 757-772 (2002). This paper concerns the existence and blow up results for the Cauchy problem for a nonlinear Schrödinger equation with isotropic harmonic potential modeling the Bose-Einstein condensation. The local problem is treated as in the case with no potential. For the global problem an evolution law, which is the analogue of the pseudo-conformal conservation law for the nonlinear Schrödinger equation, is established. With this law, the author gives wave collapse criteria, as well as an upper bound for the blow up time. A lower time for the breaking time is also given. Reviewer: Laura-Iulia Aniţa (Iaşi) Cited in 46 Documents MSC: 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 81V70 Many-body theory; quantum Hall effect 35Q55 NLS equations (nonlinear Schrödinger equations) 82B26 Phase transitions (general) in equilibrium statistical mechanics Keywords:Bose-Einstein condensation × Cite Format Result Cite Review PDF Full Text: DOI arXiv