Open Access
July/August 2011 A note on ill posedness for the KdV equation
Luc Molinet
Differential Integral Equations 24(7/8): 759-765 (July/August 2011). DOI: 10.57262/die/1356628831

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.

Citation

Download Citation

Luc Molinet. "A note on ill posedness for the KdV equation." Differential Integral Equations 24 (7/8) 759 - 765, July/August 2011. https://doi.org/10.57262/die/1356628831

Information

Published: July/August 2011
First available in Project Euclid: 27 December 2012

zbMATH: 1249.35292
MathSciNet: MR2830706
Digital Object Identifier: 10.57262/die/1356628831

Subjects:
Primary: 35A01 , 35Q53

Rights: Copyright © 2011 Khayyam Publishing, Inc.

Vol.24 • No. 7/8 • July/August 2011
Back to Top