  In [Zhang and Zheng, 2005] it was conjectured by Zhang and Zheng that
dissipative solutions of the Hunter-Saxton equation, which are known to be
unique in the class of weak solutions, dissipate the energy at the highest
possible rate. The conjecture of Zhang and Zheng was proven in [Dafermos, 2012]
by Dafermos for monotone increasing initial data with bounded energy. In this
note we prove the conjecture in [Zhang and Zheng, 2005] in full generality. To
this end we examine the evolution of the energy of any weak solution of the
Hunter-Saxton equation. Our proof shows in fact that for every time $t>0$ the
energy of the dissipative solution is not greater than the energy of any weak
solution with the same initial data.
