Global conservative solution for the periodic $\mu$-Camassa-Holm   equation
  In this paper we mainly investigate the periodic $\mu$-Camassa-Holm equation. We show the existence of global conservative solutions to the Cauchy problem of the periodic $\mu$-Camassa-Holm equation. The result is obtained by introducing a coordinate transformation into Lagrangian coordinates. Our solutions depend continuously on the initial data and has a semigroup property. 
Wei Luo, Zhaoyang Yin
math.AP