Sharp ill-posedness result for the periodic Benjamin-Ono equation

Details Sharp ill-posedness result for the periodic Benjamin-Ono equation Sharp ill-posedness result for the periodic Benjamin-Ono equation

2008-11-04

arxiv.org/abs/0811.0505v1

Journal of Functional Analysis 257 (2009) 3488-3516

Mathematics

Analysis of PDEs

Scientific paper

We prove the discontinuity for the weak $ L^2(\T) $-topology of the flow-map
associated with the periodic Benjamin-Ono equation. This ensures that this
equation is ill-posed in $ H^s(\T) $ as soon as $ s<0 $ and thus completes
exactly the well-posedness result obtained by the author.

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