Blow-up for a weakly dissipative modified two-component Camassa–Holm system

Abstract

In this paper, we study the Cauchy problem of a weakly dissipative modified two-component Camassa–Holm (MCH2) system. We first derive the precise blow-up scenario and then give several criteria guaranteeing the blow-up of the solutions. We finally discuss the blow-up rate of the blowing-up solutions.

Keywords:

• MCH2 system
• weakly dissipative
• blow-up
• blow-up rate

AMS Subject Classifications:

• 35G25
• 35L05

Acknowledgments

This work was partially supported by NNSF of China (11226181), partially supported by Projects Supported by Scientific Research Fund of SiChuan Provincial Education Department(13ZA0010), and partially supported by Natural Science Foundation Project of China West Normal University (12B024, 12A033).