Blow-up phenomena for the rotation-two-component Camassa–Holm system

Abstract

In this paper, we study blow-up phenomena for the rotation-two-component Camassa–Holm (R2CH) system, a model of equatorial water waves that includes the effect of the Coriolis force. We first derive the precise blow-up scenario for R2CH with $\sigma >0.$ Then, we present two new blow-up results for strong solutions to the system and then the precise blow-up rate for strong solutions to the system is given.

COMMUNICATED BY:

• Adrian Constantin

Keywords:

• The rotation- two-component Camassa–Holm (R2CH) system
• blow-up scenario: blow-up
• blow-up rate

2010 Mathematics Subject Classifications:

• 35B44
• 35G55
• 35L05

Acknowledgements

The author would like to thank referee(s) for his/her kindly and helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China (No. 11701525).