Well-posedness of the focusing stochastic nonlinear Schrödinger equation: $L^2$-critical and supercritical cases
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909896173158400 |
|---|---|
| author | Millet, Annie Roudenko, Svetlana |
| author_facet | Millet, Annie Roudenko, Svetlana |
| contents | We study the focusing $L^2$-critical and supercritical stochastic nonlinear Schrödinger equation subject to additive or multiplicative noise. We investigate global or long time behavior of solutions in $H^1$, which would correspond to global well-posedness in the deterministic case, with either deterministic or random initial data, and establish quantitative information about the well-posedness time, its probability and bounds on the solution in both cases. We then give criteria for finite time blow-up with positive probability for an $H^1$-valued initial data with positive energy in both cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07072 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-posedness of the focusing stochastic nonlinear Schrödinger equation: $L^2$-critical and supercritical cases Millet, Annie Roudenko, Svetlana Analysis of PDEs Probability 60H15, 35R60, 35Q35 We study the focusing $L^2$-critical and supercritical stochastic nonlinear Schrödinger equation subject to additive or multiplicative noise. We investigate global or long time behavior of solutions in $H^1$, which would correspond to global well-posedness in the deterministic case, with either deterministic or random initial data, and establish quantitative information about the well-posedness time, its probability and bounds on the solution in both cases. We then give criteria for finite time blow-up with positive probability for an $H^1$-valued initial data with positive energy in both cases. |
| title | Well-posedness of the focusing stochastic nonlinear Schrödinger equation: $L^2$-critical and supercritical cases |
| topic | Analysis of PDEs Probability 60H15, 35R60, 35Q35 |
| url | https://arxiv.org/abs/2511.07072 |