On The Free Boundary Problem Of 1d Compressible Navier-Stokes Equations With Heat Conductivity Dependent Of Temperature

The free boundary problem of one-dimensional heat conducting compressible Navier-Stokes equations with large initial data is investigated. We obtain the global existence of strong solution under stress-free boundary condition along the free surface, where the heat conductivity depends on temperature (kappa=(kappa) over bar theta(b); b2(0;1)) and the viscosity coefficient depends on density (mu=(mu) over bar (1+rho(a)), a is an element of [0,infinity)). Moreover, the large-time behavior of the free boundary for the full compressible Navier-Stokes equations is also considered when the viscosity is constant and it is first shown that the interfaces which separate the gas from vacuum will expand outwards at an algebraic rate in time for all gamma >1.