In this paper, we study the Cauchy problem of the generalized Camassa–Holm equation. Firstly, we prove the existence of the global strong solutions provide the initial data satisfying a certain sign condition. Then, we obtain the existence and the uniqueness of the global weak solutions under the same sign condition of the initial data.

中文翻译：

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广义Camassa-Holm方程的整体解

在本文中，我们研究了广义Camassa-Holm方程的Cauchy问题。首先，我们证明了全局强解的存在提供了满足一定符号条件的初始数据。然后，我们获得了在初始数据相同符号条件下全局弱解的存在性和唯一性。