Scattering for three waves nonlinear Schrödinger system with mass-resonance in 5D

In this paper, we study the dynamics behavior of the (NLS system) with three waves interaction in the energy space H 1 ( R 5 ) × H 1 ( R 5 ) × H 1 ( R 5 ) . Inspired by Dodson and Murphy (Math Res Lett 25(6):1805–1825, 2018), we establish an interaction Morawetz estimate for the (NLS system), togeth...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2023-04, Vol.62 (3), Article 92
Main Authors: Meng, Fanfei, Wang, Sheng, Xu, Chengbin
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Resonance
Resonance scattering
Systems Theory
Theoretical
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Summary:In this paper, we study the dynamics behavior of the (NLS system) with three waves interaction in the energy space H 1 ( R 5 ) × H 1 ( R 5 ) × H 1 ( R 5 ) . Inspired by Dodson and Murphy (Math Res Lett 25(6):1805–1825, 2018), 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.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-023-02435-4