Strichartz estimates for the generalized Zakharov-Kuznetsov equation on $\mathbb{R} \times \mathbb{T}$ and applications
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917145944784896 |
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| author | Nowicki-Koth, Jakob |
| author_facet | Nowicki-Koth, Jakob |
| contents | 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 $s > \frac{11}{24}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15517 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strichartz estimates for the generalized Zakharov-Kuznetsov equation on $\mathbb{R} \times \mathbb{T}$ and applications Nowicki-Koth, Jakob Analysis of PDEs 35Q53 (Primary) 35R05 (Secondary) 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 $s > \frac{11}{24}$. |
| title | Strichartz estimates for the generalized Zakharov-Kuznetsov equation on $\mathbb{R} \times \mathbb{T}$ and applications |
| topic | Analysis of PDEs 35Q53 (Primary) 35R05 (Secondary) |
| url | https://arxiv.org/abs/2506.15517 |