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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1910.02897 |
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| _version_ | 1866911967032115200 |
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| author | Cheung, Kelvin Li, Guopeng |
| author_facet | Cheung, Kelvin Li, Guopeng |
| contents | We consider the energy-critical stochastic cubic nonlinear Schrödinger equation on $\mathbb R^4$ with additive noise, and with the non-vanishing boundary conditions at spatial infinity. By viewing this equation as a perturbation to the energy-critical cubic nonlinear Schrödinger equation on $\mathbb R^4$, we prove global well-posedness in the energy space. Moreover, we establish unconditional uniqueness of solutions in the energy space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_02897 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of the 4-d energy-critical stochastic nonlinear Schrödinger equations with non-vanishing boundary condition Cheung, Kelvin Li, Guopeng Analysis of PDEs We consider the energy-critical stochastic cubic nonlinear Schrödinger equation on $\mathbb R^4$ with additive noise, and with the non-vanishing boundary conditions at spatial infinity. By viewing this equation as a perturbation to the energy-critical cubic nonlinear Schrödinger equation on $\mathbb R^4$, we prove global well-posedness in the energy space. Moreover, we establish unconditional uniqueness of solutions in the energy space. |
| title | Global well-posedness of the 4-d energy-critical stochastic nonlinear Schrödinger equations with non-vanishing boundary condition |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1910.02897 |