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


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.


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


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

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

Primary: 35A01 , 35Q53

Rights: Copyright © 2011 Khayyam Publishing, Inc.

Vol.24 • No. 7/8 • July/August 2011
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