Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913866900832256 |
|---|---|
| author | Oh, Tadahiro Wang, Yuzhao |
| author_facet | Oh, Tadahiro Wang, Yuzhao |
| contents | In a seminal paper (1996), Bourgain proved invariance of the Gibbs measure for the defocusing cubic nonlinear Schrödinger equation on the two-dimensional torus by constructing local-in-time solutions in a probabilistic manner. In this note, we revisit and streamline his argument, using the random tensor estimate developed by Deng, Nahmod, and Yue (2022). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24271 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS Oh, Tadahiro Wang, Yuzhao Analysis of PDEs Probability 35Q55, 60H15 In a seminal paper (1996), Bourgain proved invariance of the Gibbs measure for the defocusing cubic nonlinear Schrödinger equation on the two-dimensional torus by constructing local-in-time solutions in a probabilistic manner. In this note, we revisit and streamline his argument, using the random tensor estimate developed by Deng, Nahmod, and Yue (2022). |
| title | Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS |
| topic | Analysis of PDEs Probability 35Q55, 60H15 |
| url | https://arxiv.org/abs/2505.24271 |