The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices. Kenig, C. E., Ponce, G., & Vega, L. Duke Math. J., 71:1–21, 1993.
bibtex   
@ARTICLE{KPV93,
  author = {Kenig, Carlos E. and Ponce, Gustavo and Vega, Luis},
  title = {The {C}auchy problem for the {K}orteweg-de {V}ries equation in {S}obolev
	spaces of negative indices},
  journal = {Duke Math. J.},
  year = {1993},
  volume = {71},
  pages = {1--21}
}

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