## Differential and Integral Equations

### A note on ill posedness for the KdV equation

Luc Molinet

#### 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