GLOBAL CLASSICAL SOLUTION TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

doi:10.1016/S0252-9602(16)30078-9

Abstract

Abstract:

In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ) provided that the initial energy is small in some sense. In our result, we give a relation between the initial energy and the viscosity coefficient μ, and it shows that the initial energy can be large if the coefficient of the viscosity μ is taken to be large, which implies that large viscosity μ means large solution.

Key words: global existence, classical solution, compressible Navier-Stokes equations, density-dependent viscosity, vacuum

CLC Number:

35A09

Yulin YE. GLOBAL CLASSICAL SOLUTION TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY[J].Acta mathematica scientia,Series B, 2016, 36(5): 1419-1432.

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