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

作     者：Zhen Hua GUO Chang Jiang ZHU 

作者机构：Center for Nonlinear Studies and Department of Mathematics Northwest University Xi'an 710069 P. R. China Laboratory of Nonlinear Analysis Department of Mathematics Central China Normal University Wuhan 4300794 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2010年第26卷第10期

页      面：2015-2030页

核心收录：

学科分类：080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 10401012, 10771170) supported by (#10625105) the Key Laboratory of Mathematical Physics of Hubei Province 

主　　题：Compressible Navier-Stokes equations density-dependent viscosity vacuum asymptotic behavior 

摘      要：The Navier-Stokes system for one-dimensional compressible fluids with density-dependent viscosities when the initial density connects to vacuum continuously is considered in the present paper. When the viscosity coefficient u is proportional to pθ with 0 〈 θ 〈 1, the global existence and the uniqueness 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 vacuum II. J. Differential Equations, 192（2）, 475-501 （2003）]. Here p is the density. Moreover, a stabilization rate estimate for the density as t → ＋∞ for any θ 〉 0 is also given.