Geometric approach on the global conservative solutions of the Camassa-Holm equation

被引：6

作者：

Lee, Jae Min ^{[1
]}

机构：

[1] KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2019年 / 142卷

关键词：

Camassa-Holm equation; Global weak conservative solution; Global smoothness of Lagrangian trajectories; SHALLOW-WATER EQUATION; GEODESIC-FLOW; DISSIPATIVE SOLUTIONS; BREAKING WAVES;

D O I：

10.1016/j.geomphys.2019.04.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we construct global weak conservative solutions of the Camassa-Holm (CH) equation on the periodic domain. We first express the equation in Lagrangian flow variable eta and then transform it using the change of variables rho = root eta(x). The new variable removes the singularity of the CH equation, and we obtain both global weak conservative solutions and global spatial smoothness of the Lagrangian trajectories of the CH equation. This work is motivated by J. Lenells who proved similar results for the Hunter-Saxton equation using the geometric interpretation. (C) 2019 Elsevier B.V. All rights reserved.

引用

页码：137 / 150

页数：14

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