On the Cauchy problem for a four-component Camassa-Holm type system

Zeng Zhang; Zhaoyang Yin

doi:10.3934/dcds.2015.35.5153

Article Contents

2015, Volume 35, Issue 10: 5153-5169. Doi: 10.3934/dcds.2015.35.5153

This issue Previous Article Horseshoes for $\mathcal{C}^{1+\alpha}$ mappings with hyperbolic measures Next Article

On the Cauchy problem for a four-component Camassa-Holm type system

Zeng Zhang^1, and
Zhaoyang Yin^2,

1.
Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275
2.
Department of Mathematics, Zhongshan University, Guangzhou, 510275

Received: November 30, 2014

Revised: December 31, 2014

Published: September 2015

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Abstract

This paper is concerned with a four-component Camassa-Holm type system proposed in [37], where its bi-Hamiltonian structure and infinitely many conserved quantities were constructed. In the paper, we first establish the local well-posedness for the system. Then we present several global existence and blow-up results for two integrable two-component subsystems.

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

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