On Local Well-posedness of the Periodic Korteweg-de Vries Equation Below $H^{-\frac{1}{2}}(\mathbb{T})$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910709104771072 |
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| author | McConnell, Ryan Oh, Seungly |
| author_facet | McConnell, Ryan Oh, Seungly |
| contents | We utilize a modulation restricted normal form approach to establish local well-posedness of the periodic Korteweg-de Vries equation in $H^s(\mathbb{T})$ for $s> -\frac23$. This work creates an analogue of the mKdV result by Nakanishi, Takaoka, and Tsutsumi for KdV, extending the currently best-known result of $s \geq -\frac12$ without utilizing the theory of complete integrability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15069 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Local Well-posedness of the Periodic Korteweg-de Vries Equation Below $H^{-\frac{1}{2}}(\mathbb{T})$ McConnell, Ryan Oh, Seungly Analysis of PDEs 35Q53 (Primary) 37L50, 42B37 (Secondary) We utilize a modulation restricted normal form approach to establish local well-posedness of the periodic Korteweg-de Vries equation in $H^s(\mathbb{T})$ for $s> -\frac23$. This work creates an analogue of the mKdV result by Nakanishi, Takaoka, and Tsutsumi for KdV, extending the currently best-known result of $s \geq -\frac12$ without utilizing the theory of complete integrability. |
| title | On Local Well-posedness of the Periodic Korteweg-de Vries Equation Below $H^{-\frac{1}{2}}(\mathbb{T})$ |
| topic | Analysis of PDEs 35Q53 (Primary) 37L50, 42B37 (Secondary) |
| url | https://arxiv.org/abs/2411.15069 |