Global well-posedness of non-integrable hyperbolic-ellptic Ishimori system in the critical Sobolev space
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915825385996288 |
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| author | Zhang, Zexian Zhou, Yi |
| author_facet | Zhang, Zexian Zhou, Yi |
| contents | We consider the Cauchy problem for the hyperbolic-elliptic Ishimori system with general decoupling constant $κ\in \mathbb{R}$ and prove global well-posedness in the critical Sobolev space. The proof relies primarily on new bilinear estimates, which are established via a novel div-curl lemma first introduced by the second author in \cite{zhou_1+2dimensional_2022}. Our approach combines the caloric gauge technique with $U^p$-$V^p$ type Strichartz estimates to handle the hyperbolic structure of the equation. The results extend previous work on the integrable case $(κ= 1)$ to general $κ$ and provide a unified framework which also works for the hyperbolic and elliptic Schrödinger maps in dimensions $d \ge 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03576 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of non-integrable hyperbolic-ellptic Ishimori system in the critical Sobolev space Zhang, Zexian Zhou, Yi Analysis of PDEs We consider the Cauchy problem for the hyperbolic-elliptic Ishimori system with general decoupling constant $κ\in \mathbb{R}$ and prove global well-posedness in the critical Sobolev space. The proof relies primarily on new bilinear estimates, which are established via a novel div-curl lemma first introduced by the second author in \cite{zhou_1+2dimensional_2022}. Our approach combines the caloric gauge technique with $U^p$-$V^p$ type Strichartz estimates to handle the hyperbolic structure of the equation. The results extend previous work on the integrable case $(κ= 1)$ to general $κ$ and provide a unified framework which also works for the hyperbolic and elliptic Schrödinger maps in dimensions $d \ge 2$. |
| title | Global well-posedness of non-integrable hyperbolic-ellptic Ishimori system in the critical Sobolev space |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.03576 |