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

被引：40
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
相关论文
共 13 条
[1]   Global solutions of the Hunter-Saxton equation [J].
Bressan, A ;
Constantin, A .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2005, 37 (03) :996-1026
[2]   Geodesic flow on the diffeomorphism group of the circle [J].
Constantin, A ;
Kolev, B .
COMMENTARII MATHEMATICI HELVETICI, 2003, 78 (04) :787-804
[3]   ON A NONLINEAR HYPERBOLIC VARIATIONAL EQUATION .2. THE ZERO-VISCOSITY AND DISPERSION LIMITS [J].
HUNTER, JK ;
ZHENG, YX .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1995, 129 (04) :355-383
[4]   ON A NONLINEAR HYPERBOLIC VARIATIONAL EQUATION .1. GLOBAL EXISTENCE OF WEAK SOLUTIONS [J].
HUNTER, JK ;
ZHENG, YX .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1995, 129 (04) :305-353
[5]   DYNAMICS OF DIRECTOR FIELDS [J].
HUNTER, JK ;
SAXTON, R .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1991, 51 (06) :1498-1521
[6]   On a completely integrable nonlinear hyperbolic variational equation [J].
Hunter, J.K. ;
Zheng, Y. .
Physica D: Nonlinear Phenomena, 1994, 79 (2-4)
[7]   Euler equations on homogeneous spaces and Virasoro orbits [J].
Khesin, B ;
Misiolek, G .
ADVANCES IN MATHEMATICS, 2003, 176 (01) :116-144
[8]  
LENELLS J, IN PRESS J GEOM PHYS
[9]  
LENELLS J, 2006, PREPRINTS MATH SCI, V5
[10]  
MUKHERJEA A, 1984, REAL FUNCTIONAL AN A
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