标题： 陈-西蒙-希格斯方程在涡旋点的定性行为 显示英文标题

标题： The qualitative behavior at a vortex point for the Chern-Simon-Higgs equation

摘要： 在本文中，我们研究了Chern-Simon-Higgs方程在涡旋爆破点处的定性行为。 大致来说，我们将在每个这样的点建立一个能量恒等式，即局部质量是各个泡沫的和。 此外，我们证明要么只有一个泡沫，这是一个奇异泡沫，要么有超过两个泡沫，这些泡沫不包含奇异泡沫。 同时，我们证明这些泡沫的能量必须满足一个二次多项式，该多项式可用于在多重性较小时证明简单的爆破性质。 众所周知，对于许多类型的Liouville系统，Pohozaev型恒等式是一个与能量对应的二次多项式，可以直接用于计算爆破点处的局部质量。 这里的困难在于，除了能量的积分外，Chern-Simon-Higgs方程的Pohozaev型恒等式中还有一个额外项。 我们需要更详细和细致的分析来处理它。 显示英文摘要

摘要： In this paper, we study the qualitative behavior at a vortex blow-up point for Chern-Simon-Higgs equation. Roughly speaking, we will establish an energy identity at a each such point, i.e. the local mass is the sum of the bubbles. Moreover, we prove that either there is only one bubble which is a singular bubble or there are more than two bubbles which contains no singular bubble. Meanwhile, we prove that the energies of these bubbles must satisfy a quadratic polynomial which can be used to prove the simple blow-up property when the multiplicity is small. As is well known, for many Liouville type system, Pohozaev type identity is a quadratic polynomial corresponding to energies which can be used directly to compute the local mass at a blow-up point. The difficulty here is that, besides the energy's integration, there is a additional term in the Pohozaev type identity of Chern-Simon-Higgs equation. We need some more detailed and delicated analysis to deal with it.