Global well-posedness in L² for the periodic Benjamin-Ono equation

2006/01/10 by Molinet, Luc · 1 citation
#35A05 #35Q53 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0601217

Abstract

We prove that the Benjamin-Ono equation is globally well-posed in H^s(\T) for s≥ 0 . Moreover we show that the associated flow-map is Lipschitz on every bounded set of H^s(\T) , s≥ 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^∞(\T) ) cannot be of class C^1+α , α>0 , from H^s(\T) into H^s(\T) as soon as s< 0 .

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