COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY,VACUUM AND GRAVITATIONAL FORCE IN THE CASE OF GENERAL PRESSURE  

作　　者：姚磊 汪文军 

机构地区：[1]Laboratory of Nonlinear Analysis,Department of Mathematics,Central China Normal University

出　　处：《Acta Mathematica Scientia》2008年第4期801-817,共17页数学物理学报（B辑英文版）

基　　金：Program for New Century ExcellentTalents in University(NCET-04-0745);the Key Project of the National Natural Science Foundation of China(10431060)

摘　　要：This is a continuation of the article（Comm.Partial Differential Equations 26（2001）965）.In this article,the authors consider the one-dimensional compressible isentropic Navier-Stokes equations with gravitational force,fixed boundary condition,a general pressure and the density-dependent viscosity coefficient when the viscous gas connects to vacuum state with a jump in density.Precisely,the viscosity coefficient μ is proportional to ρ^θ and 0〈θ〈1/2,where ρ is the density,and the pressure P=P（ρ）is a general pressure.The global existence and the uniqueness of weak solution are proved.This is a continuation of the article（Comm.Partial Differential Equations 26（2001）965）.In this article,the authors consider the one-dimensional compressible isentropic Navier-Stokes equations with gravitational force,fixed boundary condition,a general pressure and the density-dependent viscosity coefficient when the viscous gas connects to vacuum state with a jump in density.Precisely,the viscosity coefficient μ is proportional to ρ^θ and 0〈θ〈1/2,where ρ is the density,and the pressure P=P（ρ）is a general pressure.The global existence and the uniqueness of weak solution are proved.

关 键 词：Compressible Navier-Stokes equations VACUUM a priori estimates a globalweak solution EXISTENCE 

分 类 号：O175.24[理学—数学]