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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.22924 |
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| _version_ | 1866910033885790208 |
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| author | Saut, Jean-Claude Wang, Yuexun |
| author_facet | Saut, Jean-Claude Wang, Yuexun |
| contents | This paper considers a class of non-local equations that are weakly dispersive perturbations of the inviscid Burgers equation, which includes the Fornberg-Whitham equation as a special case. We precise the known results on finite time blow-up (shock formation) by constructing a blowup solution which displays a `shock-like' singularity (called wave breaking) at one single point. Moreover, this solution converges asymptotically in the self-similar variables to a stable self-similar solution of the inviscid Burgers equation, and also possesses a Hölder $C^{1/3}$ regularity at the blowup point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22924 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Refined wave breaking for the generalized Fornberg-Whitham equation Saut, Jean-Claude Wang, Yuexun Analysis of PDEs This paper considers a class of non-local equations that are weakly dispersive perturbations of the inviscid Burgers equation, which includes the Fornberg-Whitham equation as a special case. We precise the known results on finite time blow-up (shock formation) by constructing a blowup solution which displays a `shock-like' singularity (called wave breaking) at one single point. Moreover, this solution converges asymptotically in the self-similar variables to a stable self-similar solution of the inviscid Burgers equation, and also possesses a Hölder $C^{1/3}$ regularity at the blowup point. |
| title | Refined wave breaking for the generalized Fornberg-Whitham equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.22924 |