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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.

MSC:

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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