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

• Published in: Acta mathematica scientia Vol. 28; no. 4; pp. 801 - 817
• Main Author: 姚磊 汪文军
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2008; Laboratory of Nonlinear Analysis, Department of Mathematics,Central China Normal University, Wuhan 430079, China
• Subjects: 35Q30; 76D09; a global weak solution; a priori estimates; Compressible Navier—Stokes equations; existence; Navier-Stokes方程; vacuum; 估计值; a global weak solution; a priori estimates; vacuum; existence; 35Q30; 76D09; Compressible Navier—Stokes equations; Compressible Navier-Stokes equations
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(08)60081-8

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.