2007, 18(4): 643-656. doi: 10.3934/dcds.2007.18.643

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

1. 

Department of Mathematics, University of California, Santa Barbara, CA 93106, United States

Received  October 2006 Revised  December 2006 Published  May 2007

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.
Citation: Jonatan Lenells. Weak geodesic flow and global solutions of the Hunter-Saxton equation. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 643-656. doi: 10.3934/dcds.2007.18.643
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