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arXiv · 2306.07433

A note on the well-posedness in the energy space for the generalized ZK equation posed on $\mathbb{R}\times\mathbb{T}$

Luiz Gustavo Farah·Luc Molinet
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Abstract

In this note, we prove the local well-posedness in the energy space of the $k$-generalized Zakharov-Kuznetsov equation posed on $ \R\times \T $ for any power non-linearity $ k\ge 2$. Moreover, we obtain global solutions under a precise smallness assumption on the initial data by proving a sharp Gagliardo Nirenberg type inequality.

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Luiz Gustavo Farah, Luc Molinet. 2023-06-12. A note on the well-posedness in the energy space for the generalized ZK equation posed on $\mathbb{R}\times\mathbb{T}$. https://arxiv.org/abs/2306.07433

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