A note on ill-posedness for the KdV equation

preprint2010arXivOpen access

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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A note on ill-posedness for the KdV equation

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