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

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.