# American Institute of Mathematical Sciences

November  2018, 38(11): 5523-5536. doi: 10.3934/dcds.2018243

## Global existence for a two-component Camassa-Holm system with an arbitrary smooth function

 1 School of Science, Wuhan University of Technology, Wuhan 430070, China 2 Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China 3 Faculty of Information Technology, Macau University of Science and Technology, Macau, China

* Corresponding author: Zhaoyang Yin

Received  October 2017 Revised  November 2017 Published  August 2018

Fund Project: Zhang is supported by NSFC (Grant No.: 11626177) and by the Fundamental Research Funds for the Central Universities (WUT: 2016IVA080). Yin was partially supported by NNSFC (No.11671407), FDCT (No. 098/2013/A3), Guangdong Special Support Program (No. 8-2015), and the key project of NSF of Guangdong province (No. 2016A030311004).

This paper is concerned with a two-component integrable Camassa-Holm type system with arbitrary smooth function $H$. If the function $H$ belongs to a set $\mathcal{H}$ (defined in Section 4), then we obtain the existence and uniqueness of global strong solutions and global weak solutions to the system. Our obtained results generalize and improve considerably recent results in [38,39].

Citation: Zeng Zhang, Zhaoyang Yin. Global existence for a two-component Camassa-Holm system with an arbitrary smooth function. Discrete & Continuous Dynamical Systems, 2018, 38 (11) : 5523-5536. doi: 10.3934/dcds.2018243
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