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 the global existence of strong solutions to the compressible Navier–Stokes system for a viscous and heat conducting ideal polytropic gas, when the viscosity is a constant and the heat conductivity is proportional to a positive power of the temperature. 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.