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International Mathematics Research Notices Advance Access published online on August 19, 2009
International Mathematics Research Notices, doi:10.1093/imrn/rnp133
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Well-posedness for the Generalized Benjamin–Ono Equations with Arbitrary Large Initial Data in the Critical Space

Stéphane Vento

Université Paris-Est, Laboratoire d'Analyse et de Mathématiques Appliquées, 5 bd. Descartes, Cité Descartes, Champs-Sur-Marne, 77454 Marne-La-Vallée Cedex 2, France

Correspondence: Correspondence to be sent to: stephane.vento{at}univ-paris-est.fr

We prove the local well-posedness of the generalized Benjamin–Ono equations Formula , k ≥ 4, in the scaling invariant spaces Formula where sk = 1/2 – 1/ k. Our results also hold in the nonhomogeneous spaces Formula . In the case k = 3, local well-posedness is obtained in Formula , s > 1/3.

Communicated by Prof. Carlos Kenig


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