Weak geodesic flow on a semidirect product and global solutions to the periodic Hunter-Saxton system

被引：19
作者：
Wunsch, Marcus [1 ]
机构：
[1] Swiss Fed Inst Technol, Dept Math, Zurich, Switzerland
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 15期
关键词：
The Hunter-Saxton system; Semidirect product; Weak geodesic flow; Global conservative solutions; 2-COMPONENT CAMASSA-HOLM; PROUDMAN-JOHNSON EQUATION; WELL-POSEDNESS; LIE-GROUPS; BLOW-UP; GEOMETRY; MODEL;
D O I：
10.1016/j.na.2011.04.041
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give explicit solutions for the two-component Hunter-Saxton system on the unit circle. Moreover, we show how global weak solutions can be naturally constructed using the geometric interpretation of this system as a re-expression of the geodesic flow on the semidirect product of a suitable subgroup of the diffeomorphism group of the circle with the space of smooth functions on the circle. These spatially and temporally periodic solutions turn out to be conservative. (C) 2011 Elsevier Ltd. All rights reserved.
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页码：4951 / 4960
页数：10
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