Communications in Mathematical Sciences

Volume 12 (2014)

Number 7

The existence of local solutions for the compressible Navier-Stokes equations with the density-dependent viscosities

Pages: 1277 – 1302

DOI: https://dx.doi.org/10.4310/CMS.2014.v12.n7.a6

Authors

Peixin Zhang (School of Mathematical Sciences, Huaqiao University, Quanzhou, China; School of Mathematical Sciences, Xiamen University, Xiamen, China)

Junning Zhao (School of Mathematical Sciences, Xiamen University, Xiamen, China)

Abstract

In this paper, we consider the isentropic compressible Navier-Stokes equations with density-dependent viscosities. We prove the local existence of the classical solutions, where the initial density is allowed to vanish.

Keywords

compressible Navier-Stokes equations, density-dependent viscosities, classical solution

2010 Mathematics Subject Classification

76N10

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Published 14 May 2014