论文标题
5D中的质量共振非线性Schrödinger系统的散射
Scattering For Mass-resonance Nonlinear Schrödinger System in 5D
论文作者
论文摘要
在本文中，我们通过使用B. Dodson和J. Murphy In \ cite {dodson2018}的方法来简化\ cite {hamano2018} {hamano2018}的证明。首先，我们建立一个标准，以确保解决方案散布在$ h^1（\ mathbb {r}^5）\ times h^1（\ mathbb {r}^5）$。为了验证散射标准中条件的正确性，我们必须排除原点附近的质量浓度。摩拉维斯估计的相互作用和伽利亚变换表征了衰减估计值，这意味着系统的质量不能集中。
In this paper, we simplify the proof of M. Hamano in \cite{Hamano2018}, scattering theory of the solution to \eqref{NLS system}, by using the method from B. Dodson and J. Murphy in \cite{Dodson2018}. Firstly, we establish a criterion to ensure the solution scatters in $ H^1(\mathbb{R}^5) \times H^1(\mathbb{R}^5) $. In order to verify the correctness of the condition in scattering criterion, we must exclude the concentration of mass near the origin. The interaction Morawetz estimate and Galilean transform characterize a decay estimate, which implies that the mass of the system cannot be concentrated.
