Unconditional uniqueness for the periodic Benjamin-Ono equation by normal form approach

TL;DR

This paper proves unconditional uniqueness of solutions to the periodic Benjamin-Ono equation for initial data in Sobolev spaces with regularity above 1/6, improving previous results that required higher regularity.

Contribution

It introduces a novel proof using gauge transform and time integration by parts to establish unconditional uniqueness in lower regularity spaces.

Findings

Unconditional uniqueness holds for initial data in H^s with s > 1/6.

Improves previous uniqueness results valid for s > 1/2.

Employs gauge transform and integration by parts in the proof.

Abstract

We show unconditional uniqueness of solutions to the Cauchy problem associated with the Benjamin-Ono equation under the periodic boundary condition with initial data given in $H^s$ for $s>1/6$. This improves the previous unconditional uniqueness result in $H^{1/2}$ by Molinet and Pilod (2012). Our proof is based on a gauge transform and integration by parts in the time variable.