The concept of a variational solution to the full Navier-Stokes-Fourier system is introduced in this chapter. Each equation of the complete system, that means, the equation of continuity, the momentum equation, and the energy equation, is treated separately. The basic facts of the theory of renormalized solutions of the continuity equation are reviewed. Moreover, the renormalized solutions of the thermal energy are introduced as a suitable tool to deal with possible concentrations of temperature.
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