中文摘要：

研究了一个广义两分量Camassa-Holm方程的柯西问题，该模型可从经过线性切流的浅水波的理论机制中得出．文中讨论了该模型的爆破现象，建立了爆破发生时柯西问题的初始值满足的充分条件．同时研究了强解的持久和唯一连续性．

英文摘要：

We investigate a generalized two-component Camassa-Holm system which can be derived from the theory of shallow water waves moving over a linear shear flow. We study the blow-up phenomena and establish a sufficient condition on the initial data to guarantee wave-breaking for the system. Moreover, the persistence properties of the strong solutions are also analyzed.