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

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 $s > \frac{1}{2}$.