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2010, Volume 9, Issue 4: 1041-1052. Doi: 10.3934/cpaa.2010.9.1041
This issue Previous Article Strongly nonlinear multivalued systems involving singular $\Phi$-Laplacian operators Next Article Solutions of a second-order Hamiltonian system with periodic boundary conditions

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

  • 1.

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

Received:  May 2009
Revised:  July 2009
Published:  July 2010
Abstract Related Papers Cited by
    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.
    Mathematics Subject Classification: Primary: 76N10, 76D05; Secondary: 76N15.

    Citation:
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