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### Open Access Journals

CPAA

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.

CPAA

A free-boundary problem is studied for the one-dimensional
compressible
Navier-Stokes equations with density-dependent viscosity that decreases (to zero) with decreasing density, i.e.,
$\mu=A\rho^\theta$, where $A$ and $\theta$ are positive constants.
The existence and uniqueness of the global weak
solutions are obtained with $\theta\in (0,1]$, which improves the previous
results and no vacuum is developed in the solutions in a finite
time provided the initial data does not contain vacuum.

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