A note on ill-posedness for the KdV equation

Details A note on ill-posedness for the KdV equation A note on ill-posedness for the KdV equation

2010-04-19

arxiv.org/abs/1004.3133v2

Mathematics

Analysis of PDEs

This preprint is an improved version of the previous preprint : "A remark on the ill-posedness issues for KdV and mKdV "

Scientific paper

We prove that the solution-map $ u_0 \mapsto u $ associated with the KdV
equation cannot be continuously extended in $ H^s(\R) $ for $ s<-1 $. The main
ingredients are the well-known Kato smoothing effect for the mKdV equation as
well as the Miura transform.

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