# American Institute of Mathematical Sciences

September  2016, 36(9): 5201-5221. doi: 10.3934/dcds.2016026

## Existence and uniqueness of global weak solutions of the Camassa-Holm equation with a forcing

 1 Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan 610066, China

Received  August 2015 Revised  January 2016 Published  May 2016

In this paper, we study the global well-posedness for the Camassa-Holm(C-H) equation with a forcing in $H^1(\mathbb{R})$ by the characteristic method. Due to the forcing, many important properties to study the well-posedness of weak solutions do not inherit from the C-H equation without a forcing, such as conservation laws, integrability. By exploiting the balance law and some new estimates, we prove the existence and uniqueness of global weak solutions for the C-H equation with a forcing in $H^1(\mathbb{R})$.
Citation: Shihui Zhu. Existence and uniqueness of global weak solutions of the Camassa-Holm equation with a forcing. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 5201-5221. doi: 10.3934/dcds.2016026
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