Global well-posedness of the energy-critical stochastic nonlinear Schrödinger equation on the three-dimensional torus
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909622661545984 |
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| author | Li, Guopeng Okamoto, Mamoru Tao, Liying |
| author_facet | Li, Guopeng Okamoto, Mamoru Tao, Liying |
| contents | We study the Cauchy problem of the defocusing energy-critical stochastic nonlinear Schrödinger equation (SNLS) on the three dimensional torus, forced by an additive noise. We adapt the atomic spaces framework in the context of the energy-critical nonlinear Schrödinger equation, and employ probabilistic perturbation arguments in the context of stochastic PDEs, establishing the global well-posedness of the defocusing energy-critical quintic SNLS in the energy space. It is the first global well-posedness result for the periodic SNLS in a critical space. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_15108 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of the energy-critical stochastic nonlinear Schrödinger equation on the three-dimensional torus Li, Guopeng Okamoto, Mamoru Tao, Liying Analysis of PDEs We study the Cauchy problem of the defocusing energy-critical stochastic nonlinear Schrödinger equation (SNLS) on the three dimensional torus, forced by an additive noise. We adapt the atomic spaces framework in the context of the energy-critical nonlinear Schrödinger equation, and employ probabilistic perturbation arguments in the context of stochastic PDEs, establishing the global well-posedness of the defocusing energy-critical quintic SNLS in the energy space. It is the first global well-posedness result for the periodic SNLS in a critical space. |
| title | Global well-posedness of the energy-critical stochastic nonlinear Schrödinger equation on the three-dimensional torus |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.15108 |