Self-similar blowup for the cubic Schrödinger equation
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912754538905600 |
|---|---|
| author | Donninger, Roland Schörkhuber, Birgit |
| author_facet | Donninger, Roland Schörkhuber, Birgit |
| contents | We give a rigorous proof for the existence of a finite-energy, self-similar solution to the focusing cubic Schrödinger equation in three spatial dimensions. The proof is computer-assisted and relies on a fixed point argument that shows the existence of a solution in the vicinity of a numerically constructed approximation. The latter is obtained by a standard pseudo-spectral method. The computer-assisted part of the rigorous proof uses nothing but fraction arithmetic in order to obtain quantitative bounds for the fixed point argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16597 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-similar blowup for the cubic Schrödinger equation Donninger, Roland Schörkhuber, Birgit Analysis of PDEs Mathematical Physics We give a rigorous proof for the existence of a finite-energy, self-similar solution to the focusing cubic Schrödinger equation in three spatial dimensions. The proof is computer-assisted and relies on a fixed point argument that shows the existence of a solution in the vicinity of a numerically constructed approximation. The latter is obtained by a standard pseudo-spectral method. The computer-assisted part of the rigorous proof uses nothing but fraction arithmetic in order to obtain quantitative bounds for the fixed point argument. |
| title | Self-similar blowup for the cubic Schrödinger equation |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2406.16597 |