On the Cauchy problem for nonlinear Schrödinger equations with rotation

Paolo Antonelli; Daniel Marahrens; Christof Sparber

doi:10.3934/dcds.2012.32.703

Article Contents

2012, Volume 32, Issue 3: 703-715. Doi: 10.3934/dcds.2012.32.703

This issue Previous Article Next Article Localized asymptotic behavior for almost additive potentials

On the Cauchy problem for nonlinear Schrödinger equations with rotation

1.
Department of Applied Mathematics and Theoretical Physics, CMS, Wilberforce Road, Cambridge CB3 0WA
2.
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 322 Science and Engineering Offices (M/C 249), 851 South Morgan Street, Chicago, Illinois 60607

Received: September 2010

Revised: March 2011

Published: March 2012

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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 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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Mathematics Subject Classification: Primary: 35Q55; Secondary: 35A01.

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