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On the Cauchy Problem for Nonlinear Schrodinger Equations with Rotation

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Title: On the Cauchy Problem for Nonlinear Schrodinger Equations with Rotation
Author(s): Antonelli, Paolo; Marahrens, Daniel; Sparber, Christof
Subject(s): Nonlinear Schrodinger equation Bose-Einstein condensation rotation angular momentum operator finite time blow-up
Abstract: We consider the Cauchy problem for (energy-subcritical) nonlinear Schrodinger 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.
Issue Date: 2012-03
Publisher: American Institute of Mathematical Sciences
Citation Info: Antonelli, P., Marahrens, D., & Sparber, C. 2012. On the Cauchy Problem for Nonlinear Schrodinger Equations with Rotation. Discrete and Continuous Dynamical Systems, 32(3): 703-715. doi:10.3934/dcds.2012.32.703
Type: Article
Description: © 2012 American Institute of Mathematical Sciences, originally published in the journal Discrete and Continuous Dynamical Systems - Series A. doi:10.3934/dcds.2012.32.703
URI: http://hdl.handle.net/10027/8277
ISSN: 1937-1632
Sponsor: King Abdullah University of Science and Technology (KAUST); Royal society; Cambridge European Trust; EPSRC; Grant number KUK-I1-007-43
Date Available in INDIGO: 2012-04-29
 

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