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On the Cauchy Problem for Nonlinear Schrodinger Equations with Rotation

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journal contribution
posted on 29.04.2012, 00:00 by Paolo Antonelli, Daniel Marahrens, Christof Sparber
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.

Funding

King Abdullah University of Science and Technology (KAUST); Royal society; Cambridge European Trust; EPSRC; Grant number KUK-I1-007-43

History

Publisher Statement

© 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

Publisher

American Institute of Mathematical Sciences

Language

en_US

issn

1937-1632

Issue date

01/03/2012