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July  2020, 19(7): 3769-3784. doi: 10.3934/cpaa.2020166

## Blow-up for two-component Camassa-Holm equation with generalized weak dissipation

 1 Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu, 212013, China 2 School of Mathematical Science, Nanjing Normal University, Nanjing, Jiangsu, 210023, China

*Corresponding author

Received  October 2019 Revised  January 2020 Published  April 2020

Fund Project: The first author is supported by by the National Natural Science Foundation of China(No. 11731014), and the Nature Science Foundation of Jiangsu Province(No. BK20171294)

This paper is concerned with blow-up solution for the Cauchy problem of two-component Camassa-Holm equation with generalized weak dissipation. By Kato's theorem and monotonicity, we investigate the local well-posedness of Cauchy problem and establish the blow-up criteria and the blow-up rate. Moreover, the property of blow-up points set is characterized.

Citation: Wenxia Chen, Jingyi Liu, Danping Ding, Lixin Tian. Blow-up for two-component Camassa-Holm equation with generalized weak dissipation. Communications on Pure & Applied Analysis, 2020, 19 (7) : 3769-3784. doi: 10.3934/cpaa.2020166
##### References:

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