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Global well-posedness and scattering for the coupled NLS in critical spaces.
- Source :
-
Applicable Analysis . Oct2024, Vol. 103 Issue 15, p2728-2758. 31p. - Publication Year :
- 2024
-
Abstract
- In this paper, we mainly concern with the system of the coupled nonlinear Schrödinger equation with initial data in critical spaces in dimension 3. We first obtain the global well-posedness of the solution to the coupled nonlinear Schrödinger equation with initial data in a critical space $ W^{\frac {11}{7}, \frac 76}({\mathbb {R}}^3) $ W 11 7 , 7 6 ( R 3). The key is to derive a uniform bound of a modified energy $ \mathcal {E}(t) $ E (t) based on a decomposition for the solution as in Dodson [Global well-posedness for the defocusing, cubic nonlinear Schrödinger equation with initial data in a critical space. Rev Mat Iberoam. 2022;38:1087–1100]. In addition, inspired by Dodson [Scattering for the defocusing, cubic nonlinear Schrödinger equation with initial data in a critical space. International mathematics research notices; 2023], we make a new decomposition for the solution and show the scattering to the coupled nonlinear Schrödinger equation with radially symmetric initial data in a critical Besov space $ B_{1,1}^2({\mathbb {R}}^3) $ B 1 , 1 2 ( R 3). [ABSTRACT FROM AUTHOR]
- Subjects :
- *NONLINEAR Schrodinger equation
*BESOV spaces
*NONLINEAR systems
Subjects
Details
- Language :
- English
- ISSN :
- 00036811
- Volume :
- 103
- Issue :
- 15
- Database :
- Academic Search Index
- Journal :
- Applicable Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 179941261
- Full Text :
- https://doi.org/10.1080/00036811.2024.2316621