Compressible Navier-Stokes equations with vacuum state in one dimension

Pages: 675 - 694, Volume 3, Issue 4, December 2004

doi:10.3934/cpaa.2004.3.675       Abstract        Full Text (182.8K)       Related Articles

Daoyuan Fang - Department of Mathematics, Zhejiang University, Hangzhou 310027, China (email)
Ting Zhang - Department of Mathematics, Zhejiang University, Hangzhou 310027, China (email)

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.

Keywords:  Navier-Stokes equations, vacuum, global existence of weak solutions
Mathematics Subject Classification:  35Q30.

Received: November 2003;      Revised: May 2004;      Published: September 2004.