Asymptotic Behavior of Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Vacuum

被引：58

作者：

Zhu, Changjiang ^{[1
]}

机构：

[1] Cent China Normal Univ, Dept Math, Lab Nonlinear Anal, Wuhan 430079, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2010年 / 293卷 / 01期

基金：

中国国家自然科学基金;

关键词：

DISCONTINUOUS INITIAL DATA; ONE-DIMENSIONAL EQUATIONS; GLOBAL WEAK SOLUTIONS; VISCOUS-GAS; SMOOTH SOLUTIONS; FLOW; FLUID; MOTION; CONVERGENCE; COEFFICIENT;

D O I：

10.1007/s00220-009-0914-1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we study the one-dimensional Navier-Stokes equations connecting to vacuum state with a jump in density when the viscosity depends on the density. Precisely, when the viscosity coefficient mu(rho) is proportional to rho (theta) with theta > 0, where rho is the density, we give the asymptotic behavior and the decay rate of the density function rho(x, t). Furthermore, the behavior of the density function rho(x, t) near the interfaces separating the gas from vacuum and the expanding rate of the interfaces are also studied. The analysis is based on some new mathematical techniques and some new useful estimates. This fills a final gap on studying Navier-Stokes equations with the viscosity coefficient mu(rho) dependent on the density rho.

引用

页码：279 / 299

页数：21

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