Global solutions for the generalized Camassa-Holm equation

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. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates the Cauchy problem of the generalized Camassa-Holm equation, proving the existence of global strong solutions and the existence and uniqueness of global weak solutions under a certain sign condition of the initial data.