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Scattering For Mass-resonance Nonlinear Schr\'odinger System in 5D
- Publication Year :
- 2020
-
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.
- Subjects :
- Mathematics - Analysis of PDEs
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2001.06835
- Document Type :
- Working Paper