Global Conservative Solutions to a Nonlinear Variational Wave Equation
  We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation $u_{tt} - c(u)(c(u)u_x)_x=0$, for initial data of finite energy. Here $c(\cdot)$ is any smooth function with uniformly positive bounded values. 
Alberto Bressan and Yuxi Zheng