Remarks on One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Vacuum

被引：0

作者：

Zhen Hua GUO Center for Nonlinear Studies and Department of Mathematics Northwest UniversityXian P R China Chang Jiang ZHU Laboratory of Nonlinear Analysis Department of Mathematics Central China Normal UniversityWuhan P R China ^{[710069
,4300794
]}

机构：

来源：

ActaMathematicaSinica(EnglishSeries) | 2010年 / 26卷 / 10期

关键词：

Compressible Navier-Stokes equations; density-dependent viscosity; vacuum; asymptotic behavior;

D O I：

暂无

中图分类号：

O357 [粘性流体力学]; O175 [微分方程、积分方程];

学科分类号：

080103 ; 080704 ; 070104 ;

摘要：

<正> The Navier-Stokes system for one-dimensional compressible fluids with density-dependentviscosities when the initial density connects to vacuum continuously is considered in the present paper.When the viscosity coefficient μ is proportional to ρθ with 0 < θ < 1, the global existence and theuniqueness of weak solutions are proved which improves the previous results in [Vong, S. W., Yang,T., Zhu, C. J.: Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuumⅡ. J. Differential Equations, 192（2）, 475-501 （2003）]. Here ρ is the density. Moreover, a stabilizationrate estimate for the density as t → +∞ for any θ > 0 is also given.

引用

页码：2015 / 2030

页数：16

共 9 条

[1]

Global weak solutions and asymptotic behavior to 1D compressible Navier–Stokes equations with density-dependent viscosity and vacuum[J] . Zhenhua Guo,Changjiang Zhu.Journal of Differential Equations . 2010 (11)

[2] On the barotropic compressible Navier-Stokes equations [J].

Mellet, A. ;

Vasseur, A. .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (03) :431-452

[3] GLOBAL WEAK SOLUTIONS TO 1D COMPRESSIBLE ISENTROPIC NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY [J].

Jiang, Song ;

Xin, Zhouping ;

Zhang, Ping .

METHODS AND APPLICATIONS OF ANALYSIS, 2005, 12 (03) :239-251

[4] Existence of Global Weak Solutions for a 2D Viscous Shallow Water Equations and Convergence to the Quasi-Geostrophic Model [J].

Didier Bresch ;

Benoît Desjardins .

Communications in Mathematical Physics, 2003, 238 :211-223

[5]

Compressible Navier–Stokes equations with degenerate viscosity coefficient and vacuum (II)[J] . Seak-Weng Vong,Tong Yang,Changjiang Zhu.Journal of Differential Equations . 2003 (2)

[6]

On Some Compressible Fluid Models: Korteweg, Lubrication, and Shallow Water Systems[J] . Didier Bresch,Beno?t Desjardins,Chi-Kun Lin.Communications in Partial Differential Equations . 2003 (3-4)

[7] Compressible Navier–Stokes Equations with Degenerate Viscosity Coefficient and Vacuum [J].

Tong Yang ;

Changjiang Zhu .

Communications in Mathematical Physics, 2002, 230 :329-363

[8]

A Vacuum Problem for the One-Dimensional Compressible Navier–Stokes Equations with Density-Dependent Viscosity[J] . Tong Yang,Huijiang Zhao.Journal of Differential Equations . 2002 (1)

[9] Free boundary problem for the equation of one-dimensional motion of compressible gas with density-dependent viscosity [J].

Okada M. ;

Matušů-Nečasová Š. ;

Makino T. .

Annali dell’Università di Ferrara, 2002, 48 (1) :1-20

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