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July  2010, 9(4): 1041-1052. doi: 10.3934/cpaa.2010.9.1041

Global solutions of the free boundary problem for the compressible Navier-Stokes equations with density-dependent viscosity

Xulong Qin 1, and  Zheng-An Yao 1,

1. 

Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China, China

Received  May 2009 Revised  July 2009 Published  April 2010

A free boundary problem is investigated for viscous, compressible, heat-conducting, one-dimensional real gas with general large initial data. More precisely, the viscosity is assumed to be $\mu(\rho)=\rho^{\lambda}(\lambda>0)$, where $\rho$ is the density of the gas, and there is nonlinear dependence upon the density and temperature for the equations of state which are different from the linear dependence of perfect gas. It is also proved that no shock wave, vacuum, mass or heat concentration will be developed in a finite time and that the free boundary (interface) separating the gas and vacuum expands at a finite velocity.
Keywords: density-dependent viscosity, global existence., heat-conducting real gas, initial boundary problem, Viscous.
Mathematics Subject Classification: Primary: 76N10, 76D05; Secondary: 76N1.
Citation: Xulong Qin, Zheng-An Yao. Global solutions of the free boundary problem for the compressible Navier-Stokes equations with density-dependent viscosity. Communications on Pure and Applied Analysis, 2010, 9 (4) : 1041-1052. doi: 10.3934/cpaa.2010.9.1041
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