Sharp local well-posedness for the Hirota-Satsuma system
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917468933455872 |
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| author | Deiga, Rafael |
| author_facet | Deiga, Rafael |
| contents | We establish sharp local existence results for the Hirota-Satsuma system in $H^k(\mathbb{R}) \times H^s(\mathbb{R})$, depending on the ratio between the dispersion of the components. These theorems significantly generalize previous works, which were restricted to the diagonal case of equal regularity $s=k$. Furthermore, we extend the known global well-posedness theory to the off-diagonal regime. The argument relies on the Fourier restriction norm method coupled with the concept of integrated-by-parts strong solution - a framework that generalizes the classical notion of strong solution. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_06503 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp local well-posedness for the Hirota-Satsuma system Deiga, Rafael Analysis of PDEs 35G55 (Primary) 35Q53, 35B30, 42B37 (Secondary) We establish sharp local existence results for the Hirota-Satsuma system in $H^k(\mathbb{R}) \times H^s(\mathbb{R})$, depending on the ratio between the dispersion of the components. These theorems significantly generalize previous works, which were restricted to the diagonal case of equal regularity $s=k$. Furthermore, we extend the known global well-posedness theory to the off-diagonal regime. The argument relies on the Fourier restriction norm method coupled with the concept of integrated-by-parts strong solution - a framework that generalizes the classical notion of strong solution. |
| title | Sharp local well-posedness for the Hirota-Satsuma system |
| topic | Analysis of PDEs 35G55 (Primary) 35Q53, 35B30, 42B37 (Secondary) |
| url | https://arxiv.org/abs/2605.06503 |