A bound from below for the temperature in compressible Navier–Stokes equations

We consider the full system of compressible Navier–Stokes equations for heat conducting fluid. We show that the temperature is uniformly positive for t ≥  t ₀ (for any t ₀ > 0) for any solutions with finite initial entropy. The assumptions on the viscosity and conductivity coefficients are minimal (for instance, the solutions constructed by Feireisl in (Oxford Lecture Series in Mathematics and its Applications, vol 26, 2004) verify all the requirements).