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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2602.23591 |
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| _version_ | 1866911472955686912 |
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| author | Nishitani, Tatsuo |
| author_facet | Nishitani, Tatsuo |
| contents | For hyperbolic differential operators $P$ with non-effectively hyperbolic double characteristics, we study the relationship between the Gevrey well-posedness threshold for strong well-posedness and the associated Hamilton map and flow. In our previous work, we showed that if the Hamilton map has a Jordan block of size $4$ on the double characteristic manifold $Σ$ of codimension $3$, then the Cauchy problem for $P$ is well-posed in the Gevrey class $1<s<3$ for all lower-order terms, and that this result is optimal. Moreover, if there are no bicharacterisitcs tangent to $Σ$, then the Cauchy problem is well-posed in the Gevrey class $1<s<3$ for all lower-order terms, and this result is also optimal. In the present paper, we remove the restriction on the codimension of $Σ$, thereby completing the result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23591 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A completion of our earlier work on the Cauchy problem for non-effectively hyperbolic operators Nishitani, Tatsuo Analysis of PDEs 35L For hyperbolic differential operators $P$ with non-effectively hyperbolic double characteristics, we study the relationship between the Gevrey well-posedness threshold for strong well-posedness and the associated Hamilton map and flow. In our previous work, we showed that if the Hamilton map has a Jordan block of size $4$ on the double characteristic manifold $Σ$ of codimension $3$, then the Cauchy problem for $P$ is well-posed in the Gevrey class $1<s<3$ for all lower-order terms, and that this result is optimal. Moreover, if there are no bicharacterisitcs tangent to $Σ$, then the Cauchy problem is well-posed in the Gevrey class $1<s<3$ for all lower-order terms, and this result is also optimal. In the present paper, we remove the restriction on the codimension of $Σ$, thereby completing the result. |
| title | A completion of our earlier work on the Cauchy problem for non-effectively hyperbolic operators |
| topic | Analysis of PDEs 35L |
| url | https://arxiv.org/abs/2602.23591 |