Communications in Mathematical Sciences
Volume 13 (2015)
Compressible Navier-Stokes equations with temperature dependent heat conductivity
Pages: 401 – 425
We prove the existence and uniqueness of global strong solutions to the one-dimensional, compressible Navier-Stokes system for the viscous and heat conducting ideal polytropic gas flow, when heat conductivity depends on temperature by the power law of Chapman-Enskog. The results reported in this article are valid for an initial boundary value problem with non-slip and heat insulated boundary along with smooth initial data with positive temperature and density without smallness assumption.
compressible Navier-Stokes equations, global strong solutions, uniqueness, temperature dependent heat conductivity, Chapman-Enskog law
2010 Mathematics Subject Classification