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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.23530 |
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| _version_ | 1866909762419949568 |
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| author | Cunha, Alysson |
| author_facet | Cunha, Alysson |
| contents | We prove that the Benjamin Ono equation is globally well-posed in $H^s(\mathbb{R})$ for $s > 1/2$. Our approach does not rely on the global gauge transformation introduced by Tao (arXiv:math/0307289). Instead, we employ a modified version of the standard parabolic regularization method. In particular, this technique also enables us to establish global well-posedness, in the same Sobolev space, for the dispersion-generalized Benjamin Ono (DGBO) equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23530 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Improvement of the Parabolic Regularization Method and Applications to Dispersive Models Cunha, Alysson Analysis of PDEs We prove that the Benjamin Ono equation is globally well-posed in $H^s(\mathbb{R})$ for $s > 1/2$. Our approach does not rely on the global gauge transformation introduced by Tao (arXiv:math/0307289). Instead, we employ a modified version of the standard parabolic regularization method. In particular, this technique also enables us to establish global well-posedness, in the same Sobolev space, for the dispersion-generalized Benjamin Ono (DGBO) equation. |
| title | Improvement of the Parabolic Regularization Method and Applications to Dispersive Models |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.23530 |