A note on ill-posedness for the KdV equation

Luc Molinet

A note on ill-posedness for the KdV equation

Analysis of PDEs 2010-09-16 v2

Authors: Luc Molinet

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.

Cite

@article{arxiv.1004.3133,
  title  = {A note on ill-posedness for the KdV equation},
  author = {Luc Molinet},
  journal= {arXiv preprint arXiv:1004.3133},
  year   = {2010}
}

Comments

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

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