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December  2004, 3(4): 675-694. doi: 10.3934/cpaa.2004.3.675

Compressible Navier-Stokes equations with vacuum state in one dimension

Daoyuan Fang 1, and  Ting Zhang 1,

1. 

Department of Mathematics, Zhejiang University, Hangzhou 310027, China, China

Received  November 2003 Revised  May 2004 Published  September 2004

In this paper, we consider the one-dimensional compressible Navier-Stokes equations for isentropic flow connecting to vacuum state with a continuous density when viscosity coefficient depends on the density. Precisely, the viscosity coefficient $\mu$ is proportional to $\rho^\theta$ and $0<\theta<1/2$, where $\rho$ is the density. The global existence of weak solutions is proved.
Keywords: vacuum, global existence of weak solutions, Navier-Stokes equations.
Mathematics Subject Classification: 35Q3.
Citation: Daoyuan Fang, Ting Zhang. Compressible Navier-Stokes equations with vacuum state in one dimension. Communications on Pure & Applied Analysis, 2004, 3 (4) : 675-694. doi: 10.3934/cpaa.2004.3.675
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