A note on ill-posedness for the KdV equation

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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https://hal.archives-ouvertes.fr/hal-00473966
Contributor : Luc Molinet <>
Submitted on : Wednesday, September 15, 2010 - 4:52:04 PM
Last modification on : Friday, February 15, 2019 - 1:22:22 AM
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• HAL Id : hal-00473966, version 2
• ARXIV : 1004.3133

Citation

Luc Molinet. A note on ill-posedness for the KdV equation. Differential and integral equations, Khayyam Publishing, 2011, 24 (7-8), pp.759-765. ⟨hal-00473966v2⟩

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