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Weak geodesic flow and global solutions of the Hunter-Saxton equation

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  • We show how global weak solutions of the Hunter-Saxton equation can be naturally constructed using the geometric interpretation of the equation as the Euler equation for the geodesic flow on an $L^2$-sphere. The approach involves forming a weak extension of the geodesic flow and relating it to a corresponding weak formulation of the Hunter-Saxton equation.
    Mathematics Subject Classification: Primary: 35G25, 58B20; Secondary: 53C22.


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