Weak solutions to a nonlinear variational wave equation with general data
The global existence of weak solutions is established for an initial value problem for a nonlinear variational wave equation with rather general initial data, subject to the assumption that the wave speed satisfies certain conditions. High regularity is established for the spatial derivative \(\partial_x u\) of the wave amplitude \(u\). The wave equation arises from studies of nematic liquid crystals, of long waves on a dipole chain, and elsewhere. A high space-time estimate for \(\partial_x u\) is used to enable the case of possible concentrations to be considered.
scientific article; zbMATH DE number 2165099