Local well-posedness of the Benjamin-Ono equation for a class of bounded initial data
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916272196812800 |
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| author | Jöckel, Niklas |
| author_facet | Jöckel, Niklas |
| contents | We prove local well-posedness of the Benjamin-Ono equation for a class of bounded initial data including periodic and bore-like functions. As a consequence, we obtain local well-posedness in $H^s(\mathbb{R})+H^σ(\mathbb{T})$ for $s>\frac{1}{2}$ and $σ>\frac{7}{2}$. These results follow by studying a generalized forced Benjamin-Ono equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01464 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local well-posedness of the Benjamin-Ono equation for a class of bounded initial data Jöckel, Niklas Analysis of PDEs 35Q53 We prove local well-posedness of the Benjamin-Ono equation for a class of bounded initial data including periodic and bore-like functions. As a consequence, we obtain local well-posedness in $H^s(\mathbb{R})+H^σ(\mathbb{T})$ for $s>\frac{1}{2}$ and $σ>\frac{7}{2}$. These results follow by studying a generalized forced Benjamin-Ono equation. |
| title | Local well-posedness of the Benjamin-Ono equation for a class of bounded initial data |
| topic | Analysis of PDEs 35Q53 |
| url | https://arxiv.org/abs/2402.01464 |