# American Institute of Mathematical Sciences

November  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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