A note on ill posedness for the KdV equation. (English) Zbl 1249.35292

Molinet, Luc

Differ. Integral Equ. 24, No. 7-8, 759-765 (2011).

From the text: In this note we combine the Miura transform and the so-called local Kato smoothing effect to prove that the solution-map associated with the KdV equation cannot be continuously extended in \(H^s(\mathbb {R})\) for \(s<-1\).

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
35B30	Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs

Keywords:

KdV equation; smoothing effect; Miura transform