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arXiv · 2506.15517

Strichartz estimates for the generalized Zakharov-Kuznetsov equation on $\mathbb{R} \times \mathbb{T}$ and applications

Jakob Nowicki-Koth
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Abstract

In this article, we address the Cauchy problem associated with the $k$-generalized Zakharov-Kuznetsov equation posed on $\mathbb{R} \times \mathbb{T}$. By establishing an almost optimal linear $L^4$-estimate, along with a family of bilinear refinements, we significantly lower the well-posedness threshold for all $k \geq 2$. In particular, we show that the modified Zakharov-Kuznetsov equation is locally well-posed in $H^s(\mathbb{R} \times \mathbb{T})$ for all $s > \frac{11}{24}$.

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Jakob Nowicki-Koth. 2025-06-18. Strichartz estimates for the generalized Zakharov-Kuznetsov equation on $\mathbb{R} \times \mathbb{T}$ and applications. https://arxiv.org/abs/2506.15517

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