# Local and global well-posedness of dispersion generalized Benjamin-Ono equations on the circle

## TL;DR

This paper establishes local and global well-posedness results for a family of dispersion generalized Benjamin-Ono equations on the circle, bridging the Benjamin-Ono and Korteweg-de Vries equations, with global results in $L^2$ for high dispersion.

## Contribution

It provides new well-posedness results for dispersion generalized Benjamin-Ono equations on the torus, extending understanding of their mathematical properties.

## Key findings

- Local well-posedness on the torus
- Global well-posedness in $L^2$ for high dispersion
- Connection between Benjamin-Ono and Korteweg-de Vries equations

## Abstract

New local well-posedness results for dispersion generalized Benjamin-Ono equations on the torus are proved. The family of equations under consideration links the Benjamin-Ono and Korteweg-de Vries equation. For sufficiently high dispersion global well-posedness in $L^2(\mathbb{T})$ is derived.