The Cauchy problem for a weakly dissipative 2-component Camassa-Holm system
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This article is published under the Open Access publishing model and distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0/ Please refer to the licence to obtain terms for any further reuse or distribution of this work.
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Abstract
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.
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