| Vacuum states on compressible Navier-Stokes equations with general density-dependent viscosity and general pressure law |
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| 引用本文： | Mei-man SUN Chang-jiang ZHU Laboratory of Nonlinear Analysis,Department of Mathematics,Central China Normal University,Wuhan 430079,China. Vacuum states on compressible Navier-Stokes equations with general density-dependent viscosity and general pressure law[J]. 中国科学A辑(英文版), 2007, 50(8): 1173-1185. DOI: 10.1007/s11425-007-0055-y |
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| 作者姓名： | Mei-man SUN Chang-jiang ZHU Laboratory of Nonlinear Analysis Department of Mathematics Central China Normal University Wuhan 430079 China |
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| 作者单位： | Mei-man SUN Chang-jiang ZHU Laboratory of Nonlinear Analysis，Department of Mathematics，Central China Normal University，Wuhan 430079，China |
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| 基金项目： | 国家自然科学基金;教育部新世纪优秀人才支持计划 |
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| 摘 要： | In this paper,we study the one-dimensional motion of viscous gas with a general pres- sure law and a general density-dependent viscosity coefficient when the initial density connects to the vacuum state with a jump.We prove the global existence and the uniqueness of weak solutions to the compressible Navier-Stokes equations by using the line method.For this,some new a priori estimates are obtained to take care of the general viscosity coefficientμ(ρ)instead ofρ~θ.
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| 收稿时间： | 2006-08-31 |
| 修稿时间： | 2007-01-19 |
Vacuum states on compressible Navier-Stokes equations with general density-dependent viscosity and general pressure law |
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| Mei-man Sun,Chang-jiang Zhu. Vacuum states on compressible Navier-Stokes equations with general density-dependent viscosity and general pressure law[J]. Science in China(Mathematics), 2007, 50(8): 1173-1185. DOI: 10.1007/s11425-007-0055-y |
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| Authors: | Mei-man Sun Chang-jiang Zhu |
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| Affiliation: | Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan 430079, China |
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| Abstract: | In this paper, we study the one-dimensional motion of viscous gas with a general pressure law and a general density-dependent viscosity coefficient when the initial density connects to the vacuum state with a jump. We prove the global existence and the uniqueness of weak solutions to the compressible Navier-Stokes equations by using the line method. For this, some new a priori estimates are obtained to take care of the general viscosity coefficient μ(ρ) instead of ρ θ . This work was partially supported by the Doctoral Foundation of Hebei University (Grant No. Y2006084) and the National Natural Science Foundation of China (Grant No. 10231060) |
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| Keywords: | Navier-Stokes equations density-dependent viscosity vacuum global existence |
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