Scattering For Mass-resonance Nonlinear Schrödinger System in 5D

Abstract

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.

References in corpus (2)

• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• Scattering for the quadratic nonlinear Schrödinger system in ${\mathbb{R}}^5$ without mass-resonance condition