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

doi:10.1016/S0252-9602(14)60055-2

Abstract

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) = ρ^βwith 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

CLC Number:

35A09

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.

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