数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (3): 851-871.doi: 10.1016/S0252-9602(14)60055-2

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LOCAL WELL-POSEDNESS TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

叶嵎林, 窦昌胜, 酒全森   

  1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China; School of Statistics, Capital University of Economics and Business, Beijing 100070, China;LCP, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  • 收稿日期:2013-06-28 修回日期:2013-09-09 出版日期:2014-05-20 发布日期:2014-05-20
  • 基金资助:

    The research is partially supported by China Post-doctoral Science Foundation (2012M520205); the research is partially supported by National Natural Sciences Foundation of China (11171229, 11231006) and Project of Beijing Chang Cheng Xue Zhe.

LOCAL WELL-POSEDNESS TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

 YE Yu-Lin, DOU Chang-Sheng, JIU Quan-Sen   

  1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China; School of Statistics, Capital University of Economics and Business, Beijing 100070, China;LCP, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  • Received:2013-06-28 Revised:2013-09-09 Online:2014-05-20 Published:2014-05-20
  • Supported by:

    The research is partially supported by China Post-doctoral Science Foundation (2012M520205); the research is partially supported by National Natural Sciences Foundation of China (11171229, 11231006) and Project of Beijing Chang Cheng Xue Zhe.

摘要:

In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ(ρ) = ρβ with β ≥0. Note that the initial data can be arbitrarily large to contain vacuum states.

关键词: Existence and uniqueness, classical solution, compressible Navier-Stokes equa-tions, density-dependent viscosity, vacuum

Abstract:

In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ(ρ) = ρβ with β ≥0. Note that the initial data can be arbitrarily large to contain vacuum states.

Key words: Existence and uniqueness, classical solution, compressible Navier-Stokes equa-tions, density-dependent viscosity, vacuum

中图分类号: 

  • 35A09