  We consider the compressible Navier-Stokes system where the viscosity depends
on density and the heat conductivity is proportional to a positive power of the
temperature under stress-free and thermally insulated boundary conditions.
Under the same conditions on the initial data as those of the constant
viscosity and heat conductivity case ([Kazhikhov-Shelukhin. J. Appl. Math.
Mech. 41 (1977)], we obtain the existence and uniqueness of global strong
solutions. Our result can be regarded as a natural generalization of the
Kazhikhov's theory for the constant heat conductivity case to the degenerate
and nonlinear one under stress-free and thermally insulated boundary
conditions.
