This talk focus on the motions of the nonisentropic viscous gas surrounded by the vacuum, which is modeled by the free boundary problem of the full compressible Navier-Stokes equations. The local-in-time existence and uniqueness of strong solutions in three-dimensional space are proved. The vanishing density and temperature condition is imposed on the free boundary, and the entropy is bounded.

We will also introduce a class of globally defined large solutions to the free boundary problem of compressible full Navier-Stokes equations with constant shear viscosity, vanishing bulk viscosity and heat conductivity. We establish such solutions with initial data perturbed around the self-similar solutions when the thermodynamic coefficient γ>7/6. When 7/6<γ<7/3, solutions with bounded entropy can be constructed. If, in addition, in the case when 11/9<γ<5/3, we can construct a solution as a global-in-time small perturbation of the self-similar solution and the entropy is uniformly bounded in time.