### Weak solutions to a nonlinear variational wave equation and some related problems

In this paper we present some results on the global existence of weak solutions to a nonlinear variational wave equation and some related problems. We first introduce the main tools, the ${L}^{p}$ Young measure theory and related compactness results, in the first section. Then we use the ${L}^{p}$ Young measure theory to prove the global existence of dissipative weak solutions to the asymptotic equation of the nonlinear wave equation, and comment on its relation to Camassa-Holm equations in the second section....