Full compressible Navier-Stokes equations with the Robin boundary condition on temperature

We consider full compressible Navier-Stokes equations with the Robin boundary condition on temperature. Note that the viscosity is constant and the heat conductivity is proportional to a positive power of the temperature. It is shown that a unique global strong solution existed if the initial data belongs to H-1. Subsequently, we find that the strong solution is non-linearly exponentially stable as time tends to infinity. This result could be viewed as the first one on the global well-posedness of the strong solution to full Navier-Stokes equations in a bounded domain with the degenerate heat conductivity and the Robin boundary condition on temperature. The proofs are mainly based on the energy method and a special inequality.