Global stability of superposition of viscous contact wave and rarefaction waves for compressible Navier-Stokes system with temperature-dependent transport coefficients and large data

We study the Cauchy problem for the one-dimensional full compressible Navier--Stokes equations with viscosity $μ(θ)=\tildeμθ^α$ and heat conductivity $κ(θ)=\tildeκθ^β$. For each fixed $β\ge0$, we prove the global stability of the combination of a viscous contact wave with rarefaction waves, provided