Sharp ill-posedness result for the periodic Benjamin-Ono equation
  We prove the discontinuity for the weak $ L^2(\T) $-topology of the flow-map associated with the periodic Benjamin-Ono equation. This ensures that this equation is ill-posed in $ H^s(\T) $ as soon as $ s<0 $ and thus completes exactly the well-posedness result obtained by the author. 
Luc Molinet (LMPT)