Threshold for Blowup and Stability for Nonlinear Schrödinger Equation with Rotation
Abstract
We consider the focusing NLS with an angular momentum and a harmonic potential, which models BoseEinstein condensate under a rotating magnetic trap. We give a sharp condition on the global existence and blowup in the masscritical 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 kineticmagnetic operator.
 Publication:

arXiv eprints
 Pub Date:
 February 2020
 arXiv:
 arXiv:2002.04722
 Bibcode:
 2020arXiv200204722B
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 35Q55;
 37K45;
 35P25
 EPrint:
 37 pages