Differential and Integral Equations
- Differential Integral Equations
- Volume 24, Number 7/8 (2011), 759-765.
A note on ill posedness for the KdV equation
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.
Differential Integral Equations, Volume 24, Number 7/8 (2011), 759-765.
First available in Project Euclid: 27 December 2012
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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