数学物理学报(英文版)

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

姚磊; 汪文军   

  1. 华中师范大学数学系, 武汉 430079
  • 收稿日期:2006-05-23 修回日期:2006-12-28 出版日期:2008-10-20 发布日期:2008-10-20
  • 通讯作者: 姚磊
  • 基金资助:

    Sponsored by Program for New Century Excellent Talents in University (NCET-04-0745), the Key Project of the National Natural Science Foundation of China (10431060)

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

Yao Lei; Wang Wenjun   

  1. Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan 430079, China
  • Received:2006-05-23 Revised:2006-12-28 Online:2008-10-20 Published:2008-10-20
  • Contact: Yao Lei

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 ρθ 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.

Abstract:

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 ρθ 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.

中图分类号: 

  • 35Q30