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Scattering For three waves Nonlinear Schr\'odinger System with mass-resonance in 5D
- Publication Year :
- 2022
-
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.<br />Comment: 20 pages. arXiv admin note: substantial text overlap with arXiv:2001.06835
- Subjects :
- Mathematics - Analysis of PDEs
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2201.09408
- Document Type :
- Working Paper