Global Well-Posedness for the Benjamin-Ono Equation with Small Periodic Initial Data in Analytic Spaces
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910264447729664 |
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| author | Wang, Yubo |
| author_facet | Wang, Yubo |
| contents | We establish the global well-posedness of the Benjamin--Ono equation for small, zero-mean periodic initial data in the analytic Sobolev spaces $H^{ρ,s}_0$ for integer $s \ge 1$. For sufficiently small initial data, we develop a spectral rigidification mechanism that globally preserves the analyticity radius, yielding global well-posedness without continuous dynamic loss of analyticity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27869 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global Well-Posedness for the Benjamin-Ono Equation with Small Periodic Initial Data in Analytic Spaces Wang, Yubo Analysis of PDEs 35Q35 (Primary) 35A01, 35A02, 35B65 (Secondary) We establish the global well-posedness of the Benjamin--Ono equation for small, zero-mean periodic initial data in the analytic Sobolev spaces $H^{ρ,s}_0$ for integer $s \ge 1$. For sufficiently small initial data, we develop a spectral rigidification mechanism that globally preserves the analyticity radius, yielding global well-posedness without continuous dynamic loss of analyticity. |
| title | Global Well-Posedness for the Benjamin-Ono Equation with Small Periodic Initial Data in Analytic Spaces |
| topic | Analysis of PDEs 35Q35 (Primary) 35A01, 35A02, 35B65 (Secondary) |
| url | https://arxiv.org/abs/2605.27869 |