## Differential and Integral Equations

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

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

A. Alexandrou Himonas and Carlos Kenig

#### 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

**Permanent link to this document**

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

**Mathematical Reviews number (MathSciNet)**

MR2492817

**Zentralblatt MATH identifier**

1240.35242

**Subjects**

Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]

#### Citation

Himonas, A. Alexandrou; Kenig, Carlos. Non-uniform dependence on initial data for the CH equation on the line. Differential Integral Equations 22 (2009), no. 3/4, 201--224. https://projecteuclid.org/euclid.die/1356019770.