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

被引：39
|
作者：
Lenells, Jonatan [1 ]
机构：
[1] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2007年 / 18卷 / 04期
关键词：
Hunter-Saxton equation; weak geodesic flow; global weak solutions;
D O I：
10.3934/dcds.2007.18.643
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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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页码：643 / 656
页数：14
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