The Cauchy Problem for a Weakly Dissipative 2-Component Camassa-Holm System

The weakly dissipative 2-component Camassa-Holm system is considered. A local well-posedness for the system in Besov spaces is established by using the Littlewood-Paley theory and a priori estimates for the solutions of transport equation. The wave-breaking mechanisms and the exact blow-up rate of s...

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Bibliographic Details
Published in:Mathematical problems in engineering 2014-01, Vol.2014 (1)
Main Authors: Ming, Sen, Yang, Han, Wu, Yonghong
Format: Article
Language:English
Subjects:
Cauchy problem
Cauchy problems
Dissipation
Energy dissipation
Estimates
Fluid dynamics
Function space
Mathematical analysis
Mathematical problems
Partial differential equations
Transport equations
Water waves
Wave breaking
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Summary:The weakly dissipative 2-component Camassa-Holm system is considered. A local well-posedness for the system in Besov spaces is established by using the Littlewood-Paley theory and a priori estimates for the solutions of transport equation. The wave-breaking mechanisms and the exact blow-up rate of strong solutions to the system are presented. Moreover, a global existence result for strong solutions is derived.
ISSN:1024-123X
1563-5147
DOI:10.1155/2014/801941