Threshold for Blowup and Stability for Nonlinear Schrödinger Equation with Rotation

Nyla Basharat, Hichem Hajaiej, Yi Hu, Shijun Zheng

Published 2020-02-11Version 1

We consider the focusing NLS with an angular momentum and a harmonic potential, which models Bose-Einstein condensate under a rotating magnetic trap. We give a sharp condition on the global existence and blowup in the mass-critical case. We further consider the stability of such systems via variational method. We determine that at the critical exponent $p=1+4/n$, the mass of $Q$, the ground state for the NLS with zero potential, is the threshold for both finite time blowup and orbital instability. Moreover, we prove similar results for the rotational NLS with an inhomogeneous nonlinearity. The analysis relies on the existence of ground state as well as a virial identity for the associated kinetic-magnetic operator.