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arXiv · 2201.09408

Scattering For three waves Nonlinear Schr\"odinger System with mass-resonance in 5D

Fanfei Meng·Sheng Wang·Chengbin Xu
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Abstract

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.

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Fanfei Meng, Sheng Wang, Chengbin Xu. 2022-01-24. Scattering For three waves Nonlinear Schr\"odinger System with mass-resonance in 5D. https://arxiv.org/abs/2201.09408

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