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arXiv · 2601.03576

Global well-posedness of non-integrable hyperbolic-ellptic Ishimori system in the critical Sobolev space

Zexian Zhang·Yi Zhou
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Abstract

We consider the Cauchy problem for the hyperbolic-elliptic Ishimori system with general decoupling constant $\kappa \in \mathbb{R}$ 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 $(\kappa = 1)$ to general $\kappa$ and provide a unified framework which also works for the hyperbolic and elliptic Schr\"odinger maps in dimensions $d \ge 2$.

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Zexian Zhang, Yi Zhou. 2026-01-07. Global well-posedness of non-integrable hyperbolic-ellptic Ishimori system in the critical Sobolev space. https://arxiv.org/abs/2601.03576

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