本项目主要研究两类三个分支的Camassa-Holm型系统，它们都是经典的Camassa-Holm型方程的多分支推广模型。其中第一个系统含有任意函数项，所以它其实是一个系统族。第二个系统具有N-峰孤立子。我们将利用这两个系统的结构和守恒率，通过Littlewood-Paley分解、输运方程理论、能量不等式、弱收敛方法、交换子估计等方法，来研究这两个系统Cauchy问题强解的爆破和整体存在，以及整体弱解的存在唯一性。

In this project, we mainly consider two classes of three component Camassa-Holm type systems, one with arbitrary smooth function, and the other with N-peakon solutions. They both are extension multi-component models of the classical Camassa-Holm equation. By means of the structure and the conservation laws, and by using the Littlewood-Paley decomposition, transport equation theory, energy inequalities, weak convergence method and commutator estimates, we will investigate the global existence and blow-up phenomena of strong solutions, global existence and uniqueness of weak solutions to the Cauchy problem of these two systems.