Global existence of dissipative solutions to the Hunter-Saxton equation via vanishing viscosity

被引：12

作者：

Li, Jingyu ^{[1
]}

Zhang, Kaijun ^{[1
]}

机构：

[1] NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2011年 / 250卷 / 03期

关键词：

Hunter-Saxton equation; Dissipative solution; Vanishing viscosity; L-p Young measure; HYPERBOLIC VARIATIONAL EQUATION; ASYMPTOTIC EQUATION; WAVE-EQUATION; WEAK SOLUTIONS; UNIQUENESS; SPACES;

D O I：

10.1016/j.jde.2010.08.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using the vanishing viscosity method, we prove the global existence of dissipative weak solutions to the Hunter-Saxton equation that describes the propagation of waves in a massive director field of a nematic liquid crystal. Our main tool is the L-p Young measure theory. We also derive the upper bound on the convergence rate for the vanishing viscosity approximations. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：1427 / 1447

页数：21

共 50 条

[31] A Lipschitz metric for the Hunter-Saxton equation
Carrillo, Jose Antonio
Grunert, Katrin
Holden, Helge
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2019, 44 (04) : 309 - 334
[32] Lipschitz metric for the Hunter-Saxton equation
Bressan, Alberto
Holden, Helge
Raynaud, Xavier
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2010, 94 (01): : 68 - 92
[33] GLOBAL EXISTENCE AND BLOW-UP PHENOMENA FOR THE PERIODIC HUNTER-SAXTON EQUATION WITH WEAK DISSIPATION
Wei, Xuemei
Yin, Zhaoyang
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2011, 18 (01) : 139 - 149
[34] Global Existence for the Generalized Two-Component Hunter-Saxton System
Wu, Hao
Wunsch, Marcus
JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2012, 14 (03) : 455 - 469
[35] Global weak solution for a periodic generalized Hunter-Saxton equation
Wei, Xuemei
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 391 (02) : 530 - 543
[36] Global conservative solution for the periodic dispersive Hunter-Saxton equation
Ye, Weikui
Yin, Zhaoyang
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2021, 59
[37] Uniqueness for the dispersive Hunter-Saxton equation with low regularity solutions
Ye, Huiru
Guo, Yingying
APPLICABLE ANALYSIS, 2024,
[38] On the Conservation Laws and Exact Solutions of a Modified Hunter-Saxton Equation
San, Sait
Yasar, Emrullah
ADVANCES IN MATHEMATICAL PHYSICS, 2014, 2014
[39] The Integrability of Dispersive Hunter-Saxton Equation
Fei Mingwen
JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS, 2012, 25 (04): : 330 - 334
[40] The Hunter-Saxton equation: A geometric approach
Lenells, Jonatan
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2008, 40 (01) : 266 - 277

← 1 2 3 4 5 →