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.

引用

页码：4951 / 4960

页数：10

共 50 条

[11] Wave breaking and global existence for the generalized periodic two-component Hunter-Saxton system [J].

Moon, Byungsoo ;

Liu, Yue .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 253 (01) :319-355

[12] GLOBAL ESTIMATES AND BLOW-UP CRITERIA FOR THE GENERALIZED HUNTER-SAXTON SYSTEM [J].

Sarria, Alejandro .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2015, 20 (02) :641-673

[13] Global asymptotic stabilization of the Hunter-Saxton control system [J].

Shen, Chunyu ;

Tian, Yaqi .

EUROPEAN JOURNAL OF CONTROL, 2021, 59 :129-136

[14] On the Cauchy problem of a periodic 2-component μ-Hunter-Saxton system [J].

Liu, Jingjing ;

Yin, Zhaoyang .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (01) :131-142

[15] Global Existence for the Generalized Two-Component Hunter-Saxton System [J].

Wu, Hao ;

Wunsch, Marcus .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2012, 14 (03) :455-469

[16] A Blow-up Result for the Periodic Solutions to an Integrable Dispersive Hunter-Saxton Equation [J].

Jiang, Bo .

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2022, 29 (01) :115-123

[17] REGULARITY STRUCTURE OF CONSERVATIVE SOLUTIONS TO THE HUNTER-SAXTON EQUATION [J].

Gao, Yu ;

Liu, Hao ;

Wong, Tak Kwong .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2022, 54 (01) :423-452

[18] BLOW-UP PHENOMENA AND TRAVELLING WAVE SOLUTIONS TO THE PERIODIC INTEGRABLE DISPERSIVE HUNTER-SAXTON EQUATION [J].

Li, Min ;

Yin, Zhaoyang .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2017, 37 (12) :6471-6485

[19] Blow-Up Analysis for the Periodic Two-Component μ-Hunter-Saxton System [J].

Guo, Yunxi ;

Xiong, Tingjian .

MATHEMATICAL PROBLEMS IN ENGINEERING, 2018, 2018

[20] Solitary wave solutions of the generalized two-component Hunter-Saxton system [J].

Moon, Byungsoo .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 89 :242-249

← 1 2 3 4 5 →