论文标题
旋转的非线性Schrödinger方程的爆炸和稳定性阈值
Threshold for Blowup and Stability for Nonlinear Schrödinger Equation with Rotation
论文作者
论文摘要
我们考虑具有角动量和谐波电位的聚焦NLS，该NL在旋转的磁陷阱下模拟了Bose-Einstein冷凝物。在大规模关键案件中，我们对全球存在和爆炸有鲜明的条件。我们通过变分方法进一步考虑了此类系统的稳定性。我们确定在关键指数$ p = 1+4/n $，$ q $的质量，具有零电位的NLS的基态，是有限的时间爆炸和轨道不稳定的阈值。此外，我们证明了具有不均匀性非线性的旋转NLS的明显阈值定理。该分析依赖于相关动力学操作员的基态以及病毒身份的存在。
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.
