TY - JOUR
T1 - On the Cauchy problem for nonlinear Schrödinger equations with rotation
AU - Antonelli, Paolo
AU - Marahrens, Daniel
AU - Sparber, Christof
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This publication is based on work supported by Award No. KUK-I1-007-43, funded by the King Abdullah University of Science and Technology (KAUST). C. S. acknowledges support by the Royal society through his University research fellowship. D. M. acknowledges support by the Cambridge European Trust and the EPSRC.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2011/10/21
Y1 - 2011/10/21
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/599046
UR - http://aimsciences.org//article/doi/10.3934/dcds.2012.32.703
UR - http://www.scopus.com/inward/record.url?scp=84859541270&partnerID=8YFLogxK
U2 - 10.3934/dcds.2012.32.703
DO - 10.3934/dcds.2012.32.703
M3 - Article
SN - 1078-0947
VL - 32
SP - 703
EP - 715
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
IS - 3
ER -