# American Institute of Mathematical Sciences

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

## Compressible Navier-Stokes equations with vacuum state in one dimension

 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.
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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