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We propose two models of the Boltzmann equation (BGK and Fokker-Planckmodels) for rarefied flows of thermally perfect gases. These models take intoaccount various models of energy, which are required for high temperatureflows, like for atmospheric re-entry problems. We prove that these modelssatisfy conservation and entropy properties (H-theorem), and we derive theircorresponding compressible Navier-Stokes asymptotics.

BGK and Fokker Planck Models for thermally perfect gases