A note on the well-posedness of the quartic Zakharov-Kuznetsov equation on $\mathbb{R} \times \mathbb{T}$
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910046381670400 |
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| author | Nowicki-Koth, Jakob |
| author_facet | Nowicki-Koth, Jakob |
| contents | By using a bilinear smoothing estimate recently developed in [12], together with several linear Strichartz-type estimates established therein, we improve the threshold for local well-posedness of the quartic Zakharov-Kuznetsov equation and prove that it is locally well-posed in $H^s(\mathbb{R} \times \mathbb{T})$ for all $s > \frac{1}{2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08368 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on the well-posedness of the quartic Zakharov-Kuznetsov equation on $\mathbb{R} \times \mathbb{T}$ Nowicki-Koth, Jakob Analysis of PDEs 35Q53 (Primary) 35R05 (Secondary) By using a bilinear smoothing estimate recently developed in [12], together with several linear Strichartz-type estimates established therein, we improve the threshold for local well-posedness of the quartic Zakharov-Kuznetsov equation and prove that it is locally well-posed in $H^s(\mathbb{R} \times \mathbb{T})$ for all $s > \frac{1}{2}$. |
| title | A note on the well-posedness of the quartic Zakharov-Kuznetsov equation on $\mathbb{R} \times \mathbb{T}$ |
| topic | Analysis of PDEs 35Q53 (Primary) 35R05 (Secondary) |
| url | https://arxiv.org/abs/2603.08368 |