Global well-posedness and scattering of 3D defocusing, cubic Schrödinger equation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
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2020
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| _version_ | 1866929531536801792 |
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| author | Shen, Jia Wu, Yifei |
| author_facet | Shen, Jia Wu, Yifei |
| contents | In this paper, we study the global well-posedness and scattering of 3D defocusing, cubic Schrödinger equation. Recently, Dodson [arXiv:2004.09618] studied the global well-posedness in a critical Sobolev space $\dot{W}^{11/7,7/6}$. In this paper, we aim to show that if the initial data belongs to $\dot H^\frac12$ to guarantee the local existence, then some extra weak space which is subcritical, is sufficient to prove the global well-posedness. More precisely, we prove that if the initial data belongs to $\dot{H}^{1/2}\cap \dot{W}^{s,1}$ for $12/13<s \leqslant 1$, then the corresponding solution exists globally and scatters. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2008_10019 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Global well-posedness and scattering of 3D defocusing, cubic Schrödinger equation Shen, Jia Wu, Yifei Analysis of PDEs 35Q55, 35B40 In this paper, we study the global well-posedness and scattering of 3D defocusing, cubic Schrödinger equation. Recently, Dodson [arXiv:2004.09618] studied the global well-posedness in a critical Sobolev space $\dot{W}^{11/7,7/6}$. In this paper, we aim to show that if the initial data belongs to $\dot H^\frac12$ to guarantee the local existence, then some extra weak space which is subcritical, is sufficient to prove the global well-posedness. More precisely, we prove that if the initial data belongs to $\dot{H}^{1/2}\cap \dot{W}^{s,1}$ for $12/13<s \leqslant 1$, then the corresponding solution exists globally and scatters. |
| title | Global well-posedness and scattering of 3D defocusing, cubic Schrödinger equation |
| topic | Analysis of PDEs 35Q55, 35B40 |
| url | https://arxiv.org/abs/2008.10019 |