# Global well-posedness in L^2 for the periodic Benjamin-Ono equation

Research paper by Luc Molinet

Indexed on: 02 Jul '08Published on: 02 Jul '08Published in: Mathematics - Analysis of PDEs

#### Abstract

We prove that the Benjamin-Ono equation is globally well-posed in $H^s(\T)$ for $s\ge 0$. Moreover we show that the associated flow-map is Lipschitz on every bounded set of ${\dot H}^s(\T)$, $s\ge 0$, and even real-analytic in this space for small times. This result is sharp in the sense that the flow-map (if it can be defined and coincides with the standard flow-map on $H^\infty(\T)$) cannot be of class $C^{1+\alpha}$, $\alpha>0$, from ${\dot H}^s(\T)$ into ${\dot H}^s(\T)$ as soon as $s< 0$.