This article addresses the Cauchy problem for the Zakharov-Kuznetsov equation, revealing refined bilinear estimates that improve well-posedness thresholds.
In this article, we address the Cauchy problem associated with the k-generalized Zakharov-Kuznetsov equation posed on R × T. By establishing an almost optimal linear L⁴-estimate, along with a family of bilinear refinements, we significantly lower the well-posedness threshold for all k ≥ 2. In particular, we show that the modified Zakharov-Kuznetsov equation is locally well-posed in Hˢ(R × T) for all s > 3/8.
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Jakob Nowicki-Koth (2025) studied this question.
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