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Global existence of dissipative solutions to the Hunter-Saxton equation via vanishing viscosity. (English) Zbl 1205.35228
Summary: 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 \(L^p\) Young measure theory. We also derive the upper bound on the convergence rate for the vanishing viscosity approximations.

MSC:
35Q35 PDEs in connection with fluid mechanics
35Q82 PDEs in connection with statistical mechanics
82D25 Statistical mechanical studies of crystals
76A15 Liquid crystals
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