Global strong solution to compressible Navier-Stokes equations with density dependent viscosity and temperature dependent heat conductivity

We obtain existence and uniqueness of global strong solution to one-dimensional compressible Navier-Stokes equations for ideal polytropic gas flow, with density dependent viscosity and temperature dependent heat conductivity under stress-free and thermally insulated boundary conditions. Here we assume viscosity coefficient μ(ρ)=1+ρα and heat conductivity coefficient κ(θ)=θβ for all α∈[0,∞) and β∈(0,+∞).