The existence of the global entropy weak solutions for a generalized Camassa-Holm equation

Chunxia Guan, Xi Tu, Zhaoyang Yin

In this paper, we prove the existence of a global entropy weak solution $u\in H^1(\mathbb{R})$ and ${\partial }_{x}u\in L^1(\mathbb{R})\cap BV(\mathbb{R})$ for the Cauchy problem of a…