Global Well-posedness in L for the Periodic Benjamin-ono Equation

@inproceedings{Molinet2008GlobalWI,
  title={Global Well-posedness in L for the Periodic Benjamin-ono Equation},
  author={Luc Molinet},
  year={2008}
}
We prove that the Benjamin-Ono equation is globally well-posed in Hs(T) for s ≥ 0. Moreover we show that the associated flow-map is Lipschitz on every bounded set of Hs 0 (T), s ≥ 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∞ 0 (T)) cannot be of class C , α > 0, from Hs 0(T) into H s 0(T) as soon as s < 0. 
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