Unconditional deep-water limit of the intermediate long wave equation in low-regularity
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916626362793984 |
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| author | Forlano, Justin Li, Guopeng Zhao, Tengfei |
| author_facet | Forlano, Justin Li, Guopeng Zhao, Tengfei |
| contents | In this paper, we establish the unconditional deep-water limit of the intermediate long wave equation (ILW) to the Benjamin-Ono equation (BO) in low-regularity Sobolev spaces on both the real line and the circle. Our main tool is new unconditional uniqueness results for ILW in $H^s$ when $s_0<s\leq \frac 14$ on the line and $s_0<s< \frac 12$ on the circle, where $s_0 = 3-\sqrt{33/4}\approx 0.1277$. Here, we adapt the strategy of Moşincat-Pilod (2023) for BO to the setting of ILW by viewing ILW as a perturbation of BO and making use of the smoothing property of the perturbation term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06554 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unconditional deep-water limit of the intermediate long wave equation in low-regularity Forlano, Justin Li, Guopeng Zhao, Tengfei Analysis of PDEs 35Q53, 35A02, 76B55 In this paper, we establish the unconditional deep-water limit of the intermediate long wave equation (ILW) to the Benjamin-Ono equation (BO) in low-regularity Sobolev spaces on both the real line and the circle. Our main tool is new unconditional uniqueness results for ILW in $H^s$ when $s_0<s\leq \frac 14$ on the line and $s_0<s< \frac 12$ on the circle, where $s_0 = 3-\sqrt{33/4}\approx 0.1277$. Here, we adapt the strategy of Moşincat-Pilod (2023) for BO to the setting of ILW by viewing ILW as a perturbation of BO and making use of the smoothing property of the perturbation term. |
| title | Unconditional deep-water limit of the intermediate long wave equation in low-regularity |
| topic | Analysis of PDEs 35Q53, 35A02, 76B55 |
| url | https://arxiv.org/abs/2403.06554 |