Global existence and blow-up phenomena for a weakly dissipative 2-component Camassa–Holm system

Abstract

We study the Cauchy problem of a weakly dissipative 2-component Camassa–Holm system. We first establish local well-posedness for a weakly dissipative 2-component Camassa–Holm system. We then present a global existence result for strong solutions to the system. We finally obtain several blow-up results and the blow-up rate of strong solutions to the system.

Keywords:

• a 2-component Camassa–Holm system
• weakly dissipative
• global existence
• blow-up
• blow-up rate

AMS Subject Classifications::

• 35G25
• 35L05

Acknowledgments

This study was supported by Guangdong Natural Science Foundation (No. S2011040001127). The author thanks the referees for valuable comments and suggestions.