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

Luc Molinet

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

Luc Molinet

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Abstract

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+α} $, $α>0 $, from $ {\dot H}^s(\T) $ into $ {\dot H}^s(\T) $ as soon as $ s< 0 $.

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Luc Molinet. 2008-07-02. Global well-posedness in L^2 for the periodic Benjamin-Ono equation. https://arxiv.org/abs/math/0601217

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