Summary: 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 [C. Hao, L. Hsiao
and H.-L. Li
, Math. Methods Appl. Sci. 31, No. 6, 655–664 (2008; Zbl 1132.35476
); J. Math. Phys. 48, No. 10, 102105, 11 p. (2007; Zbl 1152.81463
)]. Moreover, we find that the rotation term has a considerable influence in proving finite time blow-up in the focusing case.