On the global well-posedness for the periodic quintic nonlinear Schrödinger equation
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866929281600323584 |
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| author | Yu, Xueying Yue, Haitian |
| author_facet | Yu, Xueying Yue, Haitian |
| contents | In this paper, we consider the initial value problem for the quintic, defocusing nonlinear Schrödinger equation on $\Bbb T^2$ with general data in the critical Sobolev space $H^{\frac{1}{2}} (\Bbb T^2)$. We show that if a solution remains bounded in $H^{\frac{1}{2}} (\Bbb T^2)$ in its maximal interval of existence, then the solution is globally well-posed in $\Bbb T^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_12925 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the global well-posedness for the periodic quintic nonlinear Schrödinger equation Yu, Xueying Yue, Haitian Analysis of PDEs In this paper, we consider the initial value problem for the quintic, defocusing nonlinear Schrödinger equation on $\Bbb T^2$ with general data in the critical Sobolev space $H^{\frac{1}{2}} (\Bbb T^2)$. We show that if a solution remains bounded in $H^{\frac{1}{2}} (\Bbb T^2)$ in its maximal interval of existence, then the solution is globally well-posed in $\Bbb T^2$. |
| title | On the global well-posedness for the periodic quintic nonlinear Schrödinger equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2011.12925 |