On the Cauchy Problem for nonlinear Schrödinger equations with rotation

Details On the Cauchy Problem for nonlinear Schrödinger equations with rotation On the Cauchy Problem for nonlinear Schrödinger equations with rotation

2010-09-21

arxiv.org/abs/1009.4160v1

Mathematics

Analysis of PDEs

13 pages

Scientific paper

We consider the Cauchy problem for (energy-subcritical) nonlinear Schr\"odinger 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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