On the Cauchy problem for nonlinear Schrödinger equations with rotation

Handle URI:
http://hdl.handle.net/10754/599046
Title:
On the Cauchy problem for nonlinear Schrödinger equations with rotation
Authors:
Antonelli, Paolo; Marahrens, Daniel; Sparber, Christof
Abstract:
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.
Publisher:
American Institute of Mathematical Sciences (AIMS)
Journal:
Discrete and Continuous Dynamical Systems
Issue Date:
Oct-2011
DOI:
10.3934/dcds.2012.32.703
Type:
Article
ISSN:
1078-0947
Sponsors:
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.
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorAntonelli, Paoloen
dc.contributor.authorMarahrens, Danielen
dc.contributor.authorSparber, Christofen
dc.date.accessioned2016-02-25T13:51:49Zen
dc.date.available2016-02-25T13:51:49Zen
dc.date.issued2011-10en
dc.identifier.issn1078-0947en
dc.identifier.doi10.3934/dcds.2012.32.703en
dc.identifier.urihttp://hdl.handle.net/10754/599046en
dc.description.abstractWe 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.en
dc.description.sponsorshipThis 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.en
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en
dc.subjectBose-Einstein condensationen
dc.subjectFiangular momentum operatoren
dc.subjectFinite time blow-up.en
dc.subjectNonlinear Schrödinger equationen
dc.subjectRotationen
dc.titleOn the Cauchy problem for nonlinear Schrödinger equations with rotationen
dc.typeArticleen
dc.identifier.journalDiscrete and Continuous Dynamical Systemsen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
dc.contributor.institutionUniversity of Illinois at Chicago, Chicago, United Statesen
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