Well-posedness for the generalized Benjamin-Ono equations with arbitrary large initial data in the critical space

@inproceedings{Vento2008WellposednessFT,
  title={Well-posedness for the generalized Benjamin-Ono equations with arbitrary large initial data in the critical space},
  author={St{\'e}phane Vento},
  year={2008}
}
We prove that the generalized Benjamin-Ono equations ∂tu + H∂2 xu ± u ∂xu = 0, k ≥ 4 are locally well-posed in the scaling invariant spaces Ḣsk(R) where sk = 1/2 − 1/k. Our results also hold in the nonhomogeneous spaces Hsk(R). In the case k = 3, local well-posedness is obtained in Hs(R), s > 1/3.