Convergence rate of the vanishing viscosity limit for the Hunter-Saxton equation in the half space

被引：1

作者：

Peng, Lei ^{[1
]}

Li, Jingyu ^{[1
]}

Mei, Ming ^{[2
,3
]}

Zhang, Kaijun ^{[1
]}

机构：

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

[2] Champlain Coll St Lambert, Dept Math, St Lambert, PQ J4P 3P2, Canada

[3] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2022年 / 328卷

基金：

中国国家自然科学基金; 加拿大自然科学与工程研究理事会;

关键词：

Hunter-Saxton equation; Asymptotic analysis; Boundary layer; Well-posedness; Energy method; Vanishing viscosity limit; NAVIER-STOKES EQUATIONS; HYPERBOLIC VARIATIONAL EQUATION; BOUNDARY-LAYERS; ZERO-VISCOSITY; ASYMPTOTIC EQUATION; GLOBAL EXISTENCE; ANALYTIC SOLUTIONS; WEAK SOLUTIONS; UNIQUENESS; PERTURBATIONS;

D O I：

10.1016/j.jde.2022.04.032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the asymptotic behavior of the solutions to an initial boundary value problem of the Hunter-Saxton equation in the half space when the viscosity tends to zero. By means of the asymptotic analysis with multiple scales, we first formally derive the equations for boundary layer profiles. Next, we study the well-posedness of the equations for the boundary layer profiles by using the compactness argu-ment. Moreover, we construct an accurate approximate solution and use the energy method to obtain the convergence results of the vanishing viscosity limit.(c) 2022 Elsevier Inc. All rights reserved.

引用

页码：202 / 227

页数：26

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