论文标题
在chern-simons-schrödinger方程的阈值解决方案上
On Threshold Solutions of equivariant Chern-Simons-Schrödinger Equation
论文作者
论文摘要
我们考虑了两个空间维度的自助式Chern-Schrödinger模型。这个问题是$ l^2 $ - 临界。在模棱两可的环境下，在[Liu-Smith，2016]中证明了全球良好性和散射，以低于基态给出的一定阈值的溶液。在这项工作中，我们表明，唯一具有阈值电荷的非散射解决方案正是截至缩放，相位旋转和假符号变换的基态。我们还获得了非自身双重系统的部分结果。
We consider the self-dual Chern-Simons-Schrödinger model in two spatial dimensions. This problem is $L^2$-critical. Under equivariant setting, global wellposedness and scattering were proved in [Liu-Smith, 2016] for solution with initial charge below certain threshold given by the ground state. In this work, we show that the only non-scattering solutions with threshold charge are exactly the ground state up to scaling, phase rotation and the pseudoconformal transformation. We also obtain partial result for non-self-dual system.
