Differential and Integral Equations

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

A. Alexandrou Himonas and Carlos Kenig

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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.


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