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Vacuum states on compressible Navier-Stokes equations with general density-dependent viscosity and general pressure law

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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.

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Authors and Affiliations

  1. Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan, 430079, China

    Mei-man Sun & Chang-jiang Zhu

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  1. Mei-man Sun
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  2. Chang-jiang Zhu
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Correspondence to Chang-jiang Zhu.

Additional information

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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Sun, Mm., Zhu, Cj. Vacuum states on compressible Navier-Stokes equations with general density-dependent viscosity and general pressure law. SCI CHINA SER A 50, 1173–1185 (2007). https://doi.org/10.1007/s11425-007-0055-y

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  • DOI: https://doi.org/10.1007/s11425-007-0055-y

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