COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY,VACUUM AND GRAVITATIONAL FORCE IN THE CASE OF GENERAL PRESSURE
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 coe...
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| Published in | Acta mathematica scientia Vol. 28; no. 4; pp. 801 - 817 |
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| Main Author | |
| 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 | |
| Online Access | Get full text |
| ISSN | 0252-9602 1572-9087 |
| DOI | 10.1016/S0252-9602(08)60081-8 |
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| 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 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. |
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| AbstractList | 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. O4; 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 con-nects to vacuum state with a jump in density. Precisely, the viscosity coefficient u is proportional to pθ and 0 < θ < 1/2, where p is the density, and the pressure P =P(p) 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<ϑ½, 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. |
| Author | 姚磊 汪文军 |
| AuthorAffiliation | Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan 430079, China |
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| Cites_doi | 10.1007/BF03167921 10.1137/0151043 10.4310/MAA.2005.v12.n3.a2 10.3934/cpaa.2004.3.675 10.1007/BF03167573 10.1007/BF02824736 10.1002/mma.708 10.1002/(SICI)1097-0312(199803)51:3<229::AID-CPA1>3.0.CO;2-C 10.1016/j.jmaa.2005.05.050 10.3934/dcds.1998.4.1 10.1137/S0036141097331044 10.1081/PDE-100002385 10.1007/s00220-002-0703-6 10.1006/jdeq.2001.4140 10.1002/mma.790 10.1016/S0022-0396(03)00060-3 |
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| Keywords | a global weak solution a priori estimates vacuum existence 35Q30 76D09 Compressible Navier—Stokes equations Compressible Navier-Stokes equations |
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| Notes | Compressible Navier-Stokes equations, vacuum, a priori estimates, a globalweak solution, existence 42-1227/O O411.1 |
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| SubjectTerms | 35Q30 76D09 a global weak solution a priori estimates Compressible Navier—Stokes equations existence Navier-Stokes方程 vacuum 估计值 |
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