Sharp ill-posedness result for the periodic Benjamin–Ono equation

We prove the discontinuity for the weak L2(T)-topology of the flow-map associated with the periodic Benjamin–Ono equation. This ensures that this equation is ill-posed in Hs (T) as soon as s < 0 and thus completes exactly the well-posedness result obtained in Molinet (2008) [12]. © 2009 Elsevier Inc. All rights reserved.