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

TL;DR

This paper improves the understanding of the well-posedness of the quartic Zakharov-Kuznetsov equation on a mixed real and torus domain by establishing local well-posedness for Sobolev spaces with regularity above 1/2.

Contribution

It advances the theory by lowering the regularity threshold for local well-posedness using bilinear smoothing and Strichartz estimates.

Findings

Established local well-posedness for s > 1/2 in H^s( imes )

Utilized bilinear smoothing estimates from recent work

Improved previous regularity thresholds for the equation

Abstract

By using a bilinear smoothing estimate recently developed in [12], 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 $s > \frac{1}{2}$.