Global solutions of the Hunter–Saxton equation. (English) Zbl 1108.35024

Summary: We construct a continuous semigroup of weak, dissipative solutions to a nonlinear partial differential equation modeling nematic liquid crystals. A new distance functional, determined by a problem of optimal transportation, yields sharp estimates on the continuity of solutions with respect to the initial data.


35D05 Existence of generalized solutions of PDE (MSC2000)
49J20 Existence theories for optimal control problems involving partial differential equations
76A15 Liquid crystals
45K05 Integro-partial differential equations
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