Stochastic Perturbations in the Fractional Nonlinear Schrödinger Equation: Well-posedness and Blow-up
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918040416813056 |
|---|---|
| author | Zhang, Ao Zhang, Yanjie Duan, Jinqiao |
| author_facet | Zhang, Ao Zhang, Yanjie Duan, Jinqiao |
| contents | This work investigates radial solutions for nonlinear fractional Schrödinger equations driven by multiplicative noise. Leveraging radial deterministic and stochastic Strichartz estimates, we establish local well-posedness in the energy-subcritical regime for the stochastic fractional nonlinear Schrödinger equation. Global existence is subsequently demonstrated through stochastic evolution of mass and energy. In focusing supercritical settings, we derive blow-up criteria via localized virial inequality, revealing how multiplicative noise measurably suppresses blow-up formation compared to deterministic dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_10270 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stochastic Perturbations in the Fractional Nonlinear Schrödinger Equation: Well-posedness and Blow-up Zhang, Ao Zhang, Yanjie Duan, Jinqiao Analysis of PDEs This work investigates radial solutions for nonlinear fractional Schrödinger equations driven by multiplicative noise. Leveraging radial deterministic and stochastic Strichartz estimates, we establish local well-posedness in the energy-subcritical regime for the stochastic fractional nonlinear Schrödinger equation. Global existence is subsequently demonstrated through stochastic evolution of mass and energy. In focusing supercritical settings, we derive blow-up criteria via localized virial inequality, revealing how multiplicative noise measurably suppresses blow-up formation compared to deterministic dynamics. |
| title | Stochastic Perturbations in the Fractional Nonlinear Schrödinger Equation: Well-posedness and Blow-up |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2308.10270 |