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

Pages: 1041 - 1052, Volume 9, Issue 4, July 2010

doi:10.3934/cpaa.2010.9.1041       Abstract        Full Text (185.9K)       Related Articles

Xulong Qin - Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China (email)
Zheng-An Yao - Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China (email)

Abstract: 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:  Viscous, heat-conducting real gas, initial boundary problem,density-dependent viscosity, global existence.
Mathematics Subject Classification:  Primary: 76N10, 76D05; Secondary: 76N15.

Received: May 2009;      Revised: July 2009;      Published: April 2010.