Open AccessOn the Cauchy problem for nonlinear Schrödinger equations with rotation
Author(s) -
Paolo Antonelli,
Daniel Marahrens,
Christof Sparber
Publication year - 2012
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2012.32.703
Subject(s) - rotation (mathematics) , initial value problem , nonlinear system , physics , angular momentum , schrödinger equation , quadratic equation , cauchy problem , space (punctuation) , mathematical analysis , nonlinear schrödinger equation , momentum (technical analysis) , mathematics , mathematical physics , classical mechanics , quantum mechanics , geometry , linguistics , philosophy , finance , economics
We consider the Cauchy problem for (energy-subcritical) nonlinear Schrödinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a well-known model for superuid 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 in fiuence in proving finite time blow-up in the focusing case