  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 $H^1(\mathbb{R})$.
