Well-posedness in H^1 for the (generalized) Benjamin-Ono equation on the   circle
  We prove the local well posedness of the Benjamin-Ono equation and the generalized Benjamin-Ono equation in $ H^1(\T) $. This leads to a global well-posedness result in $ H^1(\T)$ for the Benjamin-Ono equation. 
Luc Molinet and Francis Ribaud