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.
引用
收藏
页码：643 / 656
页数：14
相关论文
共 50 条
  • [31] On the Conservation Laws and Exact Solutions of a Modified Hunter-Saxton Equation
    San, Sait
    Yasar, Emrullah
    ADVANCES IN MATHEMATICAL PHYSICS, 2014, 2014
  • [32] A Convergent Numerical Algorithm for α-Dissipative Solutions of the Hunter-Saxton Equation
    Christiansen, Thomas
    Grunert, Katrin
    Nordli, Anders
    Solem, Susanne
    JOURNAL OF SCIENTIFIC COMPUTING, 2024, 99 (01)
  • [33] The Integrability of Dispersive Hunter-Saxton Equation
    Fei Mingwen
    JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS, 2012, 25 (04): : 330 - 334
  • [34] The Hunter-Saxton equation: A geometric approach
    Lenells, Jonatan
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2008, 40 (01) : 266 - 277
  • [35] Novel symmetric structures and explicit solutions to a coupled Hunter-Saxton equation
    Zhao, Qiulan
    Wang, Huanjin
    Li, Xinyue
    PHYSICA SCRIPTA, 2023, 98 (06)
  • [36] Global Conservative Solutions of the Two-Component μ-Hunter-Saxton System
    Shi, Xiayang
    Liu, Jingjing
    Zhang, Hongyang
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2021, 2021
  • [37] ON THE CAUCHY PROBLEM OF THE MODIFIED HUNTER-SAXTON EQUATION
    Mi, Yongsheng
    Mu, Chunlai
    Zheng, Pan
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2016, 9 (06): : 2047 - 2072
  • [38] Poisson structure of a modified Hunter-Saxton equation
    Lenells, Jonatan
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2008, 41 (28)
  • [39] DISSIPATIVE NUMERICAL METHODS FOR THE HUNTER-SAXTON EQUATION
    Yan Xu Department of Mathematics
    JournalofComputationalMathematics, 2010, 28 (05) : 606 - 620
  • [40] Convergent difference schemes for the Hunter-Saxton equation
    Holden, H.
    Karlsen, K. H.
    Risebro, N. H.
    MATHEMATICS OF COMPUTATION, 2007, 76 (258) : 699 - 744
12345