Articles

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
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  • 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 date: 2013-06-28

  Revised date: 2013-09-09

  Online 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.

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.

Cite this article

YE Yu-Lin , DOU Chang-Sheng , JIU Quan-Sen . LOCAL WELL-POSEDNESS TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY[J]. Acta mathematica scientia, Series B, 2014 , 34(3) : 851 -871 . DOI: 10.1016/S0252-9602(14)60055-2

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