  We give a proof for the uniqueness of dissipative solution for the
Camassa-Holm equation with some peakon-antipeakon initial data following
Dafermos' earlier resut in [5] on the Hunter-Saxton equation. Our result shows
that two existing global existence frameworks, through the vanishing viscosity
method by Xin-Zhang in [11] and the transformation of coordinate method for
dissipative solutions by Bressan-Constantin in [3], give the same solution, for
a special but typical initial data forming finite time gradient blowup.
