Remarks on nonlinear Schrödinger equations arising on rotational Bose-Einstein condensates. (English) Zbl 1479.35774
Author’s abstract: In this paper, we study the Cauchy problem for nonlinear Schrödinger equations arising as an effective model of the Bose-Einstein condensate in a magnetic trap rotating with an angular velocity. We first establish sufficient conditions showing the existence of global-in-time and finite time blow-up solutions to the equation. We next derive sharp thresholds for global existence versus finite time blow-up in the mass-critical and mass-supercritical cases. We also study the existence and strong instability of ground state standing waves related to the equation. Finally we prove the existence, non-existence, and orbital stability of prescribed mass standing waves when the rotational speed is smaller than a critical value.
Reviewer: Johanna Michor (Wien)
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35B44 | Blow-up in context of PDEs |
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