A note on the well-posedness in the energy space for the generalized ZK equation posed on ℝ×\mathbbT

2023/06/12 by Luiz Gustavo Farah, Luc Molinet, Farah, Luiz Gustavo +1 · 1 citation
Mathematics · #35A01 #35Q53 #35Q60 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2306.07433

openalex publication_date 2023/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we prove the local well-posedness in the energy space of the k-generalized Zakharov-Kuznetsov equation posed on \R× \T for any power non-linearity k≥ 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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• Strichartz estimates for the generalized Zakharov-Kuznetsov equation on ℝ × \mathbbT and applications

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