A note on the well-posedness of the quartic Zakharov-Kuznetsov equation on $ \mathbb{R} \times \mathbb{T} $

Jakob Nowicki-Koth; Jakob Nowicki-Koth

doi:10.3934/math.20261008

AIMS Mathematics

2026, Volume 11, Issue 8: 25090-25099. doi: 10.3934/math.20261008

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Research article

A note on the well-posedness of the quartic Zakharov-Kuznetsov equation on $ \mathbb{R} \times \mathbb{T} $

Jakob Nowicki-Koth ^,

Mathematisches Institut der Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany

Received: 13 March 2026 Revised: 23 June 2026 Accepted: 02 July 2026 Published: 14 August 2026
MSC : 35Q53, 35R05

By using a bilinear smoothing estimate recently developed in ^[1], 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} $.
- generalized Zakharov-Kuznetsov equation,
- semiperiodic domain,
- low regularity well-posedness theory,
- Strichartz estimates,
- fixed-point iteration
Citation: Jakob Nowicki-Koth. A note on the well-posedness of the quartic Zakharov-Kuznetsov equation on $ \mathbb{R} \times \mathbb{T} $[J]. AIMS Mathematics, 2026, 11(8): 25090-25099. doi: 10.3934/math.20261008

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Abstract

By using a bilinear smoothing estimate recently developed in ^[1], 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} $.

References

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