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2007, Volume 18, Issue 4: 643-656. Doi: 10.3934/dcds.2007.18.643

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

Jonatan Lenells^1,

1.
Department of Mathematics, University of California, Santa Barbara, CA 93106

Received: October 2006

Revised: December 2006

Published: October 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 35G25, 58B20; Secondary: 53C22.

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