Initial data problems for the two-component Camassa-Holm system

Initial data problems for the two-component Camassa-Holm system

This article concerns the study of some properties of the two-component Camassa-Holm system. By constructing two sequences of solutions of the two-component Camassa-Holm system, we prove that the solution map of the Cauchy problem of the two-component Camassa-Holm system is not uniformly continu...

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Bibliographic Details
Main Author: Xiaohuan Wang
Format: Article
Language:English
Published: Texas State University 2014-06-01
Series:Electronic Journal of Differential Equations
Subjects:
Non-uniform dependence
Camassa-Holm system
well-posedness
energy estimates
initial value problem
Online Access:http://ejde.math.txstate.edu/Volumes/2014/148/abstr.html
Description
Summary:This article concerns the study of some properties of the two-component Camassa-Holm system. By constructing two sequences of solutions of the two-component Camassa-Holm system, we prove that the solution map of the Cauchy problem of the two-component Camassa-Holm system is not uniformly continuous in $H^s(\mathbb{R})$, $s>5/2$.
ISSN:1072-6691

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