Well-posedness and blow-up for a modified two-component Camassa–Holm equation

Abstract

In this article, we consider a newly modified two-component Camassa–Holm equation. First, we establish the local well-posedness result, then we present a precise blow-up scenario. Afterwards, we derive a new conservation law, by which and the precise blow-up scenario we prove three blow-up results and a blow-up rate estimate result.

Keywords:

• modified two-component Camassa–Holm equation
• local well-posedness
• blow up

AMS Subject Classifications:

• 35G25
• 35L05

Acknowledgements

The author expresses his gratitude to Professor Mingxin Wang for his enthusiastic guidance and constant encouragement. This work was supported by PRC Grants NSFC 10771032.