Threshold for Blowup and Stability for Nonlinear Schr\"odinger Equation with Rotation
Abstract
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 , the mass of , the ground state for the NLS with zero potential, is the threshold for both finite time blowup and orbital instability. Moreover, we prove a sharp threshold theorem 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.
Keywords
Cite
@article{arxiv.2002.04722,
title = {Threshold for Blowup and Stability for Nonlinear Schr\"odinger Equation with Rotation},
author = {Nyla Basharat and Hichem Hajaiej and Yi Hu and Shijun Zheng},
journal= {arXiv preprint arXiv:2002.04722},
year = {2023}
}
Comments
44 pages. Theorem 1.2 is improved to a sharp version concerning RNLS with an inhomogeneous nonlinearity. Among others, examples are provided to verify the blow-up criteria in Lemma 4.1. A few references are updated