# On the Cauchy problem for higher dimensional Benjamin-Ono and Zakharov-Kuznetsov equations

## TL;DR

This paper studies a family of dispersive equations connecting higher dimensional Benjamin-Ono and Zakharov-Kuznetsov equations, establishing new well-posedness results through advanced mathematical techniques.

## Contribution

It introduces new well-posedness results for fractional Zakharov-Kuznetsov equations using transversality and frequency localization methods.

## Key findings

- Proved well-posedness for a family of dispersive equations.
- Established techniques applicable to fractional higher-dimensional equations.
- Enhanced understanding of dispersive equation behavior in higher dimensions.

## Abstract

A family of dispersive equations is considered which links a higher dimensional Benjamin-Ono equation and the Zakharov-Kuznetsov equation. For these fractional Zakharov-Kuznetsov equations new well-posedness results are proved using transversality and localization of time to small frequency dependent time intervals.