|
|||||
 |
|
|
|
|
|
|
|
Scattering of the
three-dimensional cubic nonlinear Schrödinger equation with
partial harmonic potentials
Xing Cheng, Chang-Yu Guo, Zihua Guo, Xian Liao and Jia Shen |
|
Vol. 17 (2024), No. 10, 3371–3446
|
 |
Abstract |
|
|
We consider the following three-dimensional defocusing cubic nonlinear Schrödinger equation (NLS) with partial harmonic potential: Our main result shows that the solution scatters for any given initial data with finite mass and energy. The main new ingredient in our approach is to approximate (NLS) in the large-scale case by a relevant dispersive continuous resonant (DCR) system. The proof of global well-posedness and scattering of the new (DCR) system is greatly inspired by the fundamental works of Dodson (2012, 2016) in his study of scattering for the mass-critical nonlinear Schrödinger equation. The analysis of (DCR) system allows us to utilize the additional regularity of the smooth nonlinear profile so that the celebrated concentration-compactness/rigidity argument of Kenig and Merle (2006, 2008) applies. |
Keywords
Schrödinger equation, scattering, partial harmonic
potentials, dispersive continuous resonant system, profile
decomposition
|
Mathematical Subject Classification
Primary: 35Q55, 35P25, 35B40
|
Milestones
Received: 12 April 2021
Revised: 20 July 2022
Accepted: 31 August 2023
Published: 21 November 2024
|
Authors |
| Xing Cheng | |
| School of Mathematics Hohai University Nanjing China |
|
| Chang-Yu Guo | |
| Research Center for Mathematics and
Interdisciplinary Sciences Shandong University Qingdao China |
Department of Physics and
Mathematics University of Eastern Finland Joensuu Finland |
| Zihua Guo | |
| School of Mathematics Monash University Clayton, VIC Australia |
|
| Xian Liao | |
| Institute for Analysis Karlsruhe Institute of Technology Karlsruhe Germany |
|
| Jia Shen | |
| School of Mathematical Sciences and
LPMC Nankai University Tianjin China |
|
| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
