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arXiv · 1004.3133

A note on ill-posedness for the KdV equation

Luc Molinet
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Abstract

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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Luc Molinet. 2010-09-15. A note on ill-posedness for the KdV equation. https://arxiv.org/abs/1004.3133

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