Invariant Gibbs dynamics for the nonlinear Schrödinger equations on the disc
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_ | 1866911161607258112 |
|---|---|
| author | Forlano, Justin Wang, Yuzhao |
| author_facet | Forlano, Justin Wang, Yuzhao |
| contents | We consider the two-dimensional defocusing nonlinear Schrödinger equation (NLS) on the unit disc in the plane with the Gibbs initial data under radial symmetry. By using a type of random averaging operator ansatz, we build a strong local-in-time solution theory, and thus prove almost sure global well-posedness and invariance of the Gibbs measure via Bourgain's invariant measure argument. This work completes the program initiated by Tzvetkov (2006, 2008) on the construction of invariant Gibbs dynamics (of strong solutions) for NLS on the disc. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14861 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Invariant Gibbs dynamics for the nonlinear Schrödinger equations on the disc Forlano, Justin Wang, Yuzhao Analysis of PDEs 35Q55, 35R01, 35R60, 37K99 We consider the two-dimensional defocusing nonlinear Schrödinger equation (NLS) on the unit disc in the plane with the Gibbs initial data under radial symmetry. By using a type of random averaging operator ansatz, we build a strong local-in-time solution theory, and thus prove almost sure global well-posedness and invariance of the Gibbs measure via Bourgain's invariant measure argument. This work completes the program initiated by Tzvetkov (2006, 2008) on the construction of invariant Gibbs dynamics (of strong solutions) for NLS on the disc. |
| title | Invariant Gibbs dynamics for the nonlinear Schrödinger equations on the disc |
| topic | Analysis of PDEs 35Q55, 35R01, 35R60, 37K99 |
| url | https://arxiv.org/abs/2509.14861 |