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

[21] On the Cauchy problem for a weakly dissipative generalized -Hunter-Saxton equation
Wang, Feng
Li, Fengquan
Chen, Qiaoling
MONATSHEFTE FUR MATHEMATIK, 2016, 181 (03): : 715 - 744
[22] The Hunter-Saxton equation with noise
Holden, Helge
Karlsen, Kenneth H.
Pang, Peter H. C.
JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 270 : 725 - 786
[23] Several Types of Similarity Solutions for the Hunter-Saxton Equation
Mathew Baxter
Robert A.Van Gorder
Kuppalapalle Vajravelu
Communications in Theoretical Physics, 2015, 63 (06) : 675 - 681
[24] The modified Hunter-Saxton equation
Gorka, Przemyslaw
Reyes, Enrique G.
JOURNAL OF GEOMETRY AND PHYSICS, 2012, 62 (08) : 1793 - 1809
[25] REGULARITY STRUCTURE OF CONSERVATIVE SOLUTIONS TO THE HUNTER-SAXTON EQUATION
Gao, Yu
Liu, Hao
Wong, Tak Kwong
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2022, 54 (01) : 423 - 452
[26] ASYMPTOTIC BEHAVIOR OF CONSERVATIVE SOLUTIONS TO THE HUNTER-SAXTON EQUATION
Gao, Yu
Liu, Hao
Wong, Tak kwong
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2023, 55 (05) : 5483 - 5525
[27] The Periodic Boundary Value Problem for the Weakly Dissipative μ-Hunter-Saxton Equation
Ouyang, Zhengyong
Wang, Xiangdong
Rong, Haiwu
ADVANCES IN MATHEMATICAL PHYSICS, 2015, 2015
[28] GENERALIZED CHARACTERISTICS AND THE HUNTER-SAXTON EQUATION
Dafermos, Constantine M.
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2011, 8 (01) : 159 - 168
[29] Wave breaking and global existence for a weakly dissipative generalized two-component μ-Hunter-Saxton system
Wang, Feng
Li, Fengquan
Chen, Qiaoling
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2015, 23 : 61 - 77
[30] Lipschitz stability for the Hunter-Saxton equation
Grunert, Katrin
Tandy, Matthew
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2022, 19 (02) : 275 - 310

← 1 2 3 4 5 →