Long Time Well-posedness for the Benjamin-Ono Equation with Quasi-Periodic Initial Data
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917553602822144 |
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| author | Wang, Yubo |
| author_facet | Wang, Yubo |
| contents | This paper investigates the long time well-posedness of the Benjamin-Ono (BO) equation with quasi-periodic initial data in analytic space. We demonstrate that the Lax operator of the BO equation exhibits a trivial spectrum, and elucidate the fundamental mathematical obstacles to establishing global well-posedness.
Furthermore, by employing Tao's gauge transformation in conjunction with the Birkhoff Normal Form method, we extend the lifespan of the solutions to $O(ε^{-3})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01778 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Long Time Well-posedness for the Benjamin-Ono Equation with Quasi-Periodic Initial Data Wang, Yubo Analysis of PDEs 35Q53, 35A01, 35B34 This paper investigates the long time well-posedness of the Benjamin-Ono (BO) equation with quasi-periodic initial data in analytic space. We demonstrate that the Lax operator of the BO equation exhibits a trivial spectrum, and elucidate the fundamental mathematical obstacles to establishing global well-posedness. Furthermore, by employing Tao's gauge transformation in conjunction with the Birkhoff Normal Form method, we extend the lifespan of the solutions to $O(ε^{-3})$. |
| title | Long Time Well-posedness for the Benjamin-Ono Equation with Quasi-Periodic Initial Data |
| topic | Analysis of PDEs 35Q53, 35A01, 35B34 |
| url | https://arxiv.org/abs/2606.01778 |