Global wellposedness of the modified Benjamin-Ono equation with initial data in H 1 / 2

@inproceedings{Kenig2005GlobalWO,
  title={Global wellposedness of the modified Benjamin-Ono equation with initial data in H 1 / 2},
  author={Carlos E. Kenig and Hideo Takaoka},
  year={2005}
}
We prove that the modified Benjamin-Ono equation is globally wellposed in H for s ≥ 1/2. The exponent H seems to be optimal in the sense that the solution map is not C in H for s < 1/2 [18]. We perform a gauge transformation as in T. Tao [27], but we combine it with a Littlewood-Paley decomposition. We also use a space-time L-estimate that it is able to handle solutions in H instead of solutions in the Besov space B 1/2 2,1 [18]. 

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