The IVP for certain dispersion generalized of the ZK equation in the cylinder space

TL;DR

This paper proves well-posedness for a generalized dispersion Zakharov-Kutnesov equation in cylindrical space using localized Strichartz estimates and compactness arguments.

Contribution

It introduces new well-posedness results for the dispersion generalized ZK equation in cylindrical geometry, employing novel analytical techniques.

Findings

Established well-posedness in cylindrical space

Developed localized Strichartz estimates for the equation

Applied compactness methods to prove existence and uniqueness

Abstract

We establish well-posedness for the Cauchy problem associated to the dispersion generalized Zakharov-Kutnesov equation in the cylinder. Our main ingredient is a localized Strichartz estimate and an argument of compactness