Differential and Integral Equations

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(\mathbb R) $ for $ s<-1 $. The main ingredients are the well-known Kato smoothing effect for the mKdV equation as well as the Miura transform.

Article information

Source
Differential Integral Equations, Volume 24, Number 7/8 (2011), 759-765.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356628831

Mathematical Reviews number (MathSciNet)
MR2830706

Zentralblatt MATH identifier
1249.35292

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 35A01: Existence problems: global existence, local existence, non-existence

Citation

Molinet, Luc. A note on ill posedness for the KdV equation. Differential Integral Equations 24 (2011), no. 7/8, 759--765. https://projecteuclid.org/euclid.die/1356628831


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