ZERO DISSIPATION LIMIT TO RAREFACTION WAVE WITH VACUUM FOR ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS

被引：39

作者：

Huang, Feimin ^{[1
,2
]}

Li, Mingjie ^{[3
]}

Wang, Yi ^{[1
,2
]}

机构：

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

[2] Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China

[3] Minzu Univ China, Coll Sci, Beijing 100081, Peoples R China

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2012年 / 44卷 / 03期

关键词：

compressible Navier-Stokes equations; zero dissipation limit; rarefaction wave; vacuum; PIECEWISE-SMOOTH SOLUTIONS; VANISHING VISCOSITY LIMIT; CONSERVATION-LAWS; EULER EQUATIONS; VISCOUS LIMITS; SYSTEMS; FLOW;

D O I：

10.1137/100814305

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is well-known that one-dimensional isentropic gas dynamics has two elementary waves, i.e., shock wave and rarefaction wave. Among the two waves, only the rarefaction wave can be connected to a vacuum. Given a rarefaction wave with one-side vacuum state to the compressible Euler equations, we can construct a sequence of solutions to one-dimensional compressible isentropic Navier-Stokes equations which converge to the above rarefaction wave with vacuum as the viscosity tends to zero. Moreover, the uniform convergence rate is obtained. The proof consists of a scaling argument and elementary energy analysis based on the underlying rarefaction wave structures.

引用

页码：1742 / 1759

页数：18

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