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Article Dans Une Revue American Journal of Mathematics Année : 2008

Global well-posedness in L^2 for the periodic Benjamin-Ono equation

Résumé

We prove that the Benjamin-Ono equation is globally well-posed in $ H^s(\T) $ for $ s\ge 0 $. Moreover we show that the associated flow-map is Lipschitz on every bounded set of $ {\dot H}^s(\T) $, $s\ge 0$, 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^\infty(\T) $) cannot be of class $ C^{1+\alpha} $, $\alpha>0 $, from $ {\dot H}^s(\T) $ into $ {\dot H}^s(\T) $ as soon as $ s< 0 $.
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Dates et versions

hal-00016752 , version 1 (10-01-2006)
hal-00016752 , version 2 (02-07-2008)

Identifiants

Citer

Luc Molinet. Global well-posedness in L^2 for the periodic Benjamin-Ono equation. American Journal of Mathematics, 2008, 130 (3), pp.635-683. ⟨hal-00016752v2⟩
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