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 \( \mathbb {R}\times \mathbb {T}\) 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.

关于在 $$\mathbb {R}times\mathbb {T}$$ 上提出的广义 ZK 方程在能量空间中的良好提出性的说明
在本论文中,我们证明了对于任意幂非线性 \( k\ge 2\) 的 k 广义扎哈罗夫-库兹涅佐夫方程在能量空间中的局部良好求解性。此外,我们通过证明一个尖锐的加利亚尔多-尼伦堡式不等式,在初始数据的精确小性假设下得到了全局解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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