The Cauchy problem for the Benjamin-Ono equation in $L^2$ revisited

TL;DR

This paper offers a simplified proof of the well-posedness of the Benjamin-Ono equation in L^2, extending results to stronger uniqueness and unconditional well-posedness in H^s for s>1/4.

Contribution

It provides a simpler proof of existing results and establishes unconditional well-posedness in H^s for s>1/4, strengthening prior work.

Findings

Simplified proof of well-posedness in L^2

Unconditional well-posedness in H^s for s>1/4

Stronger uniqueness results

Abstract

In a recent work, Ionescu and Kenig proved that the Cauchy problem associatedto the Benjamin-Ono equation is well-posed in $L^2(\mathbb R)$. In this paper we give a simpler proof of Ionescu and Kenig's result, which moreover provides stronger uniqueness results. In particular, we prove unconditional well-posedness in $H^s(\mathbb R)$, for $s>1/4$.