Scattering For three waves Nonlinear Schrödinger System with mass-resonance in 5D

2022/01/24 by Fanfei Meng, Sheng Wang, Meng, Fanfei +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum Chromodynamics and Particle Interactions #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2201.09408

openalex publication_date 2022/01/24 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the dynamics behavior of the NLS system with three waves interaction in the energy space H¹(ℝ⁵) × H¹(ℝ⁵)× H¹(ℝ⁵) . Inspired by B. Dodson and J. Murphy in \citeDodson2018, 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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• Threshold solutions for the energy-critical NLS system with quadratic interaction

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