Global existence of dissipative solutions to the Hunter–Saxton equation via vanishing viscosity

Using the vanishing viscosity method, we prove the global existence of dissipative weak solutions to the Hunter–Saxton equation that describes the propagation of waves in a massive director field of a nematic liquid crystal. Our main tool is the Lp Young measure theory. We also derive the upper bound on the convergence rate for the vanishing viscosity approximations.