Global well-posedness and scattering for the defocusing septic one-dimensional NLS via new smoothing and almost Morawetz estimates
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866907973773688832 |
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| author | Lee, Zachary Yu, Xueying |
| author_facet | Lee, Zachary Yu, Xueying |
| contents | In this paper, we show that the one dimensional septic nonlinear Schrödinger equation is globally well-posed and scatters in $H^s (\mathbb{R})$ when $s > 19/54$. We prove new smoothing estimates on the nonlinear Duhamel part of the solution and utilize a linear-nonlinear decomposition to take advantage of the gained regularity. We also prove new $L^{p+3}_{t,x}$ almost Morawetz estimates for the defocusing $p-$NLS adapted to the low-regularity setting, before specializing to the septic case $p=7$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07234 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness and scattering for the defocusing septic one-dimensional NLS via new smoothing and almost Morawetz estimates Lee, Zachary Yu, Xueying Analysis of PDEs 35Q55 In this paper, we show that the one dimensional septic nonlinear Schrödinger equation is globally well-posed and scatters in $H^s (\mathbb{R})$ when $s > 19/54$. We prove new smoothing estimates on the nonlinear Duhamel part of the solution and utilize a linear-nonlinear decomposition to take advantage of the gained regularity. We also prove new $L^{p+3}_{t,x}$ almost Morawetz estimates for the defocusing $p-$NLS adapted to the low-regularity setting, before specializing to the septic case $p=7$. |
| title | Global well-posedness and scattering for the defocusing septic one-dimensional NLS via new smoothing and almost Morawetz estimates |
| topic | Analysis of PDEs 35Q55 |
| url | https://arxiv.org/abs/2407.07234 |