论文标题
在5D中具有质量共振的三个波的散射非线性schrödinger系统
Scattering For three waves Nonlinear Schrödinger System with mass-resonance in 5D
论文作者
论文摘要
在本文中，我们研究了在能量空间中具有三个波相互作用的NLS系统的动态行为$ h^1（\ Mathbb {r}^5）\ times h^1（\ Mathbb {r}^5）\ times h^1（\ Mathbb {r}^5）$。受到B. Dodson和J. Murphy的启发，我们在{Dodson2018}中为NLS系统建立了一个相互作用的Morawetz估计值，以及Tao-Dodson-Murphy证明的标准 - 我们可以将散射在能量空间的基态下与大量共鸣。在径向假设下，我们可以消除质量共振条件。
In this paper, we study the dynamics behavior of the NLS system with three waves interaction in the energy space $H^1(\mathbb{R}^5) \times H^1(\mathbb{R}^5)\times H^1(\mathbb{R}^5) $. Inspired by B. Dodson and J. Murphy in \cite{Dodson2018}, we establish an interaction Morawetz estimate for the NLS system, together with the criterion which proved by Tao-Dodson--Murphy we can get the scattering under the ground state in energy space with mass-resonance. Under the radial assumption, we can remove the mass-resonance condition.
