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

الملخص EN

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.