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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/2605.05033 |
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| _version_ | 1866913094958055424 |
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| author | Geba, Dan-Andrei Himonas, A. Alexandrou Holliman, Curtis |
| author_facet | Geba, Dan-Andrei Himonas, A. Alexandrou Holliman, Curtis |
| contents | This article proves norm inflation in the critical Sobolev space $H^{3/2}(\mathbb{R})$ for the $b$-Novikov equation, which is a $1$-parameter family of Camassa-Holm-type equations with cubic nonlinearities. This result completes the well-posedness theory for this equation, which was previously known to be locally well-posed in $H^{s}(\mathbb{R})$ for $s>3/2$ and ill-posed in $H^{s}(\mathbb{R})$ for $s<3/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05033 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ill-posedness in the critical Sobolev space for the $b$-Novikov equation Geba, Dan-Andrei Himonas, A. Alexandrou Holliman, Curtis Analysis of PDEs 35Q53, 37K10 This article proves norm inflation in the critical Sobolev space $H^{3/2}(\mathbb{R})$ for the $b$-Novikov equation, which is a $1$-parameter family of Camassa-Holm-type equations with cubic nonlinearities. This result completes the well-posedness theory for this equation, which was previously known to be locally well-posed in $H^{s}(\mathbb{R})$ for $s>3/2$ and ill-posed in $H^{s}(\mathbb{R})$ for $s<3/2$. |
| title | Ill-posedness in the critical Sobolev space for the $b$-Novikov equation |
| topic | Analysis of PDEs 35Q53, 37K10 |
| url | https://arxiv.org/abs/2605.05033 |