Global well-posedness for the k-dispersion generalized Benjamin-Ono equation

TL;DR

This paper proves global well-posedness in the energy space for the supercritical k-dispersion generalized Benjamin-Ono equation, establishing sharp data conditions and extending results to the generalized Benjamin-Ono equation.

Contribution

It provides the first sharp conditions for global well-posedness in the supercritical regime for this family of nonlinear dispersive equations.

Findings

Global well-posedness established under sharp data conditions

Results extended to the generalized Benjamin-Ono equation

Conditions are optimal for the energy space

Abstract

We consider the $k$-dispersion generalized Benjamin-Ono equation in the supercritical case. We establish sharp conditions on the data to show global well-posedness in the energy space for this family of nonlinear dispersive equations. We also prove similar results for the generalized Benjamin-Ono equation.