English

On the Cauchy Problem for nonlinear Schr\"odinger equations with rotation

Analysis of PDEs 2013-02-08 v1 Mathematical Physics math.MP

Abstract

We consider the Cauchy problem for (energy-subcritical) nonlinear Schr\"odinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a well-known model for superfluid quantum gases in rotating traps. We prove global existence (in the energy space) for defocusing nonlinearities without any restriction on the rotation frequency, generalizing earlier results given in [11,12]. Moreover, we find that the rotation term has a considerable influence in proving finite time blow-up in the focusing case.

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Cite

@article{arxiv.1009.4160,
  title  = {On the Cauchy Problem for nonlinear Schr\"odinger equations with rotation},
  author = {Paolo Antonelli and Daniel Marahrens and Christof Sparber},
  journal= {arXiv preprint arXiv:1009.4160},
  year   = {2013}
}

Comments

13 pages

R2 v1 2026-06-21T16:17:06.938Z