## Differential and Integral Equations

### Non-uniform dependence on initial data for a family of non-linear evolution equations

Erika A. Olson

#### Abstract

We show that solutions to the periodic Cauchy problem for a family of non-linear evolution equations, which contains the Camassa-Holm equation, do not depend uniformly continuously on initial data in the Sobolev space $H^s(\mathbb{T})$, when $s=1$ or $s\geq 2$.

#### Article information

Source
Differential Integral Equations, Volume 19, Number 10 (2006), 1081-1102.

Dates
First available in Project Euclid: 21 December 2012

https://projecteuclid.org/euclid.die/1356050310

Mathematical Reviews number (MathSciNet)
MR2278671

Zentralblatt MATH identifier
1212.35426

Subjects