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 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 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.

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

References in corpus (4)

• The Nonexistence of Vortices for Rotating Bose-Einstein Condensates with Attractive Interactions
• Stability and instability properties of rotating Bose-Einstein condensates
• Nonlinear Schrödinger Equations for Bose-Einstein Condensates
• Blow-up dynamics and spectral property in the $L^2$-critical nonlinear Schrödinger equation in high dimensions

Cited by in corpus (1)

• On stability of rotational 2D binary Bose-Einstein condensates