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

Global Strong Solutions to Compressible Navier-Stokes System with Degenerate Heat Conductivity and Density-Depending Viscosity