Global existence and local well-posedness for a three-component Camassa-Holm system with N-peakon solutions

In this paper we mainly investigate the Cauchy problem of a three-component Camassa-Holm system. We first prove the local well-posedness of the system in Besov spaces Bp,rs with p,r∈[1,∞], s>max⁡{1p,12} by using the Littlewood-Paley theory and transport equations theory. Then, we establish two blow-up criteria which along with the conservation laws enable us to study global existence. Moreover, if the initial data satisfies some certain sign conditions, we obtain a global existence result. Finally, we verify that the system possesses peakon solutions.