Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (5): 1419-1432.doi: 10.1016/S0252-9602(16)30078-9

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

Yulin YE   

  1. School of Mathematics and Statistics, Henan University, Kaifeng 475004, China
  • Received:2015-01-29 Revised:2015-05-30 Online:2016-10-25 Published:2016-10-25
  • Contact: Yulin YE,nkyelin@163.com E-mail:nkyelin@163.com

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
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