Compressible Navier-Stokes equations with vacuum state in one dimension

Daoyuan Fang; Ting Zhang

doi:10.3934/cpaa.2004.3.675

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2004, Volume 3, Issue 4: 675-694. Doi: 10.3934/cpaa.2004.3.675

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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

Received: October 31, 2003

Revised: April 30, 2004

Published: November 2004

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Abstract

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.

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Mathematics Subject Classification: 35Q30.

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