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

Zeng Zhang; Zhaoyang Yin

doi:10.3934/dcds.2018243

Article Contents

2018, Volume 38, Issue 11: 5523-5536. Doi: 10.3934/dcds.2018243

This issue Previous Article Orbital stability of peakons for a modified Camassa-Holm equation with higher-order nonlinearity Next Article Large data global regularity for the classical equivariant Skyrme model

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

Zeng Zhang^1, and
Zhaoyang Yin^2,3, ,

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
* Corresponding author: Zhaoyang Yin

Received: September 30, 2017

Revised: October 31, 2017

Published: August 2018

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)

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Abstract

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].

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Mathematics Subject Classification: Primary: 35G25; Secondary: 35L05.

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