Vanishing Viscosity Limit of the Compressible Navier-Stokes Equations for Solutions to a Riemann Problem

被引：53

作者：

Huang, Feimin ^{[1
]}

Wang, Yi ^{[1
]}

Yang, Tong ^{[2
]}

机构：

[1] Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China

[2] City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2012年 / 203卷 / 02期

关键词：

PIECEWISE-SMOOTH SOLUTIONS; ZERO-DISSIPATION LIMIT; RAREFACTION WAVES; ASYMPTOTIC STABILITY; EULER EQUATIONS; VISCOUS LIMITS; SYSTEMS;

D O I：

10.1007/s00205-011-0450-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the vanishing viscosity limit of the compressible Navier-Stokes equations to the Riemann solution of the Euler equations that consists of the superposition of a shock wave and a rarefaction wave. In particular, it is shown that there exists a family of smooth solutions to the compressible Navier-Stokes equations that converges to the Riemann solution away from the initial and shock layers at a rate in terms of the viscosity and the heat conductivity coefficients. This gives the first mathematical justification of this limit for the Navier-Stokes equations to the Riemann solution that contains these two typical nonlinear hyperbolic waves.

引用

页码：379 / 413

页数：35

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