Electron. J. Diff. Equ., Vol. 2014 (2014), No. 148, pp. 1-15.

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

Xiaohuan Wang

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 $H^s(\mathbb{R})$, $s>5/2$.

Submitted June 4, 2014. Published June 24, 2014.
Math Subject Classifications: 35G25, 35B30, 35L05.
Key Words: Non-uniform dependence; Camassa-Holm system; well-posedness; energy estimates; initial value problem.

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Xiaohuan Wang
College of Mathematics and Information Science
Henan University
Kaifeng 475001, China
email: xhwangmaths@163.com
Phone: 86+15226038672

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