Global solutions of the Hunter-Saxton equation
classification
🧮 math.AP
keywords
solutionsconstructcontinuitycontinuouscrystalsdatadetermineddifferential
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We construct a continuous semigroup of weak, dissipative solutions to a nonlinear partial differential equations 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.
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