STABILITY OF VISCOUS SHOCK WAVES FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

doi:10.1016/S0252-9602(15)30076-X

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (1): 34-48.doi: 10.1016/S0252-9602(15)30076-X

STABILITY OF VISCOUS SHOCK WAVES FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

何躏, 唐少君, 王涛

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

收稿日期:2015-02-03 修回日期:2015-05-20 出版日期:2016-01-30 发布日期:2016-01-30
通讯作者: Shaojun TANG,E-mail:shaojun.tang@whu.edu.cn E-mail:shaojun.tang@whu.edu.cn
作者简介:Lin He,E-mail:Linhe1989@whu.edu.cn;Tao WANG,E-mail:tao.wang@whu.edu.cn
基金资助:
This work was supported by "the Fundamental Research Funds for the Central Universities".

STABILITY OF VISCOUS SHOCK WAVES FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

Lin HE, Shaojun TANG, Tao WANG

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received:2015-02-03 Revised:2015-05-20 Online:2016-01-30 Published:2016-01-30
Contact: Shaojun TANG,E-mail:shaojun.tang@whu.edu.cn E-mail:shaojun.tang@whu.edu.cn
Supported by:
This work was supported by "the Fundamental Research Funds for the Central Universities".

摘要/Abstract

摘要：

We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density-dependent viscosity. The nonlinear stability of the viscous shock waves is shown for certain class of large initial perturbation with integral zero which can allow the initial density to have large oscillation. Our analysis relies upon the technique developed by Kanel' and the continuation argument.

关键词: viscous shock waves, density-dependent viscosity, one-dimensional compressible Navier-Stokes equations, nonlinear stability, large density oscillation

Abstract:

Key words: viscous shock waves, density-dependent viscosity, one-dimensional compressible Navier-Stokes equations, nonlinear stability, large density oscillation

中图分类号:

35B35

何躏, 唐少君, 王涛. STABILITY OF VISCOUS SHOCK WAVES FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY[J]. 数学物理学报(英文版), 2016, 36(1): 34-48.

Lin HE, Shaojun TANG, Tao WANG. STABILITY OF VISCOUS SHOCK WAVES FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY[J]. Acta mathematica scientia,Series B, 2016, 36(1): 34-48.

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STABILITY OF VISCOUS SHOCK WAVES FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

STABILITY OF VISCOUS SHOCK WAVES FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

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