Global Existence of Strong Solutions to Compressible Navier-Stokes System with Degenerate Heat Conductivity in Unbounded Domains

Abstract

In one-dimensional unbounded domains, we prove global existence of strong solutions to the compressible Navier-Stokes system for a viscous and heat conducting ideal polytropic gas, when the viscosity is constant and the heat conductivity $\kappa$ depends on the temperature $\theta$ according to $\kappa=\bar\kappa\theta^\beta (\beta>0)$. Note that the conditions imposed on the initial data are the same as those of the constant heat conductivity case ([Kazhikhov, A. V. Siberian Math. J. 23 (1982), 44-49]) and can be arbitrarily large. Therefore, our result generalizes Kazhikhov's result for the constant heat conductivity case to the degenerate and nonlinear one.