## Differential and Integral Equations

### Non-uniform dependence on initial data for the CH equation on the line

#### Abstract

For $s > 1$ two sequences of CH solutions living in a bounded subset of the Sobolev space $H^s(\mathbb{R})$ are constructed, whose distance at the initial time is converging to zero while at any later time it is bounded below by a positive constant. This implies that the solution map of the CH equation is not uniformly continuous in $H^s(\mathbb{R})$.

#### Article information

Source
Differential Integral Equations, Volume 22, Number 3/4 (2009), 201-224.

Dates
First available in Project Euclid: 20 December 2012

https://projecteuclid.org/euclid.die/1356019770

Mathematical Reviews number (MathSciNet)
MR2492817

Zentralblatt MATH identifier
1240.35242

Subjects