Scattering For Mass-resonance Nonlinear Schrödinger System in 5D

2020/01/19 by Fanfei Meng, Chengbin Xu, Meng, Fanfei +1 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2001.06835

openalex publication_date 2020/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we simplify the proof of M. Hamano in \citeHamano2018, scattering theory of the solution to \eqrefNLS system, by using the method from B. Dodson and J. Murphy in \citeDodson2018. Firstly, we establish a criterion to ensure the solution scatters in H¹(ℝ⁵) × H¹(ℝ⁵) . 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.

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• Dynamics of the Energy-Critical Nonlinear Schrödinger System in \mathbb R⁴

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