Deep-water limit of the intermediate long wave equation in $L^2$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910525685760000 |
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| author | Chapouto, Andreia Li, Guopeng Oh, Tadahiro Pilod, Didier |
| author_facet | Chapouto, Andreia Li, Guopeng Oh, Tadahiro Pilod, Didier |
| contents | We study the well-posedness issue of the intermediate long wave equation (ILW) on both the real line and the circle. By applying the gauge transform for the Benjamin-Ono equation (BO) and adapting the $L^2$ well-posedness argument for BO by Molinet and the fourth author (2012), we prove global well-posedness of ILW in $L^2$ on both the real line and the circle. In the periodic setting, this provides the first low regularity well-posedness of ILW. We then establish convergence of the ILW dynamics to the BO dynamics in the deep-water limit at the $L^2$-level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_07997 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Deep-water limit of the intermediate long wave equation in $L^2$ Chapouto, Andreia Li, Guopeng Oh, Tadahiro Pilod, Didier Analysis of PDEs 35Q35 We study the well-posedness issue of the intermediate long wave equation (ILW) on both the real line and the circle. By applying the gauge transform for the Benjamin-Ono equation (BO) and adapting the $L^2$ well-posedness argument for BO by Molinet and the fourth author (2012), we prove global well-posedness of ILW in $L^2$ on both the real line and the circle. In the periodic setting, this provides the first low regularity well-posedness of ILW. We then establish convergence of the ILW dynamics to the BO dynamics in the deep-water limit at the $L^2$-level. |
| title | Deep-water limit of the intermediate long wave equation in $L^2$ |
| topic | Analysis of PDEs 35Q35 |
| url | https://arxiv.org/abs/2311.07997 |