Conservative solutions to a system of variational wave equations

We investigate a system of variational wave equations which is the Euler–Lagrange equations of a variational principle arising in the theory of nematic liquid crystals and a few other physical contexts. We establish the global existence of an energy-conservative weak solution to its Cauchy problem for initial data of finite energy. The main difficulty arises from the possible concentration of energy. We construct the solution by introducing a new set of variables depending on the energy, whereby all singularities are resolved.