Well-posedness in energy space for the periodic modified Benjamin-Ono equation

TL;DR

This paper establishes local well-posedness of the periodic modified Benjamin-Ono equation in the energy space, leading to global well-posedness in the defocusing case, using $X^{s,b}$ analysis after a gauge transform.

Contribution

It proves local well-posedness in the energy space for the periodic modified Benjamin-Ono equation, a significant step in understanding its well-posedness properties.

Findings

Local well-posedness in $H^{1/2}$ energy space

Global well-posedness in the defocusing case

Application of $X^{s,b}$ analysis after gauge transform

Abstract

We prove that the periodic modified Benjamin-Ono equation is locally well-posed in the energy space $H^{1/2}$. This ensures the global well-posedness in the defocusing case. The proof is based on an $X^{s,b}$ analysis of the system after gauge transform.