Norm inflation and low-regularity ill-posedness for the rod equation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915985792958464 |
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| author | Li, Jinlu Yu, Yanghai |
| author_facet | Li, Jinlu Yu, Yanghai |
| contents | In this paper, we consider the Cauchy problem for the rod equation in the line. By constructing an explicit smooth initial data, we present a new method to prove that this problem is ill-posed in $H^s(\R)$ with $1< s<3/2$ in the sense of {\it norm inflation}, i.e., an initial data is smooth and arbitrarily small in $H^s(\R)$ with $1< s<3/2$, but the solution becomes arbitrarily large in the Sobolev space after an arbitrarily short time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12423 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Norm inflation and low-regularity ill-posedness for the rod equation Li, Jinlu Yu, Yanghai Analysis of PDEs In this paper, we consider the Cauchy problem for the rod equation in the line. By constructing an explicit smooth initial data, we present a new method to prove that this problem is ill-posed in $H^s(\R)$ with $1< s<3/2$ in the sense of {\it norm inflation}, i.e., an initial data is smooth and arbitrarily small in $H^s(\R)$ with $1< s<3/2$, but the solution becomes arbitrarily large in the Sobolev space after an arbitrarily short time. |
| title | Norm inflation and low-regularity ill-posedness for the rod equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.12423 |