Starting from a Boltzmann kinetic model for a gas mixture with bimolecular chemical reaction, hydrodynamic equations at Euler level are deduced by a consistent hydrodynamic limit in the presence of resonance, namely when the fast process driving evolution is constituted by elastic scattering between particles of the same species. The structure of the resulting multi-temperature and multi-velocity fluid-dynamic description is briefly commented on, and some results in closed analytical form are given for the special case of Maxwellian collision kernel.

Abstract. The slip boundary conditions for the compressible Navier-Stokes equations are derived systematically from the Boltzmann equation on the basis of the ChapmanEnskog solution of the Boltzmann equation and the analysis of the Knudsen layer adjacent to the boundary. The resulting formulas of the slip boundary conditions are summarized with explicit values of the slip coefficients for hard-sphere molecules as well as the Bhatnagar-Gross-Krook (BGK) model. These formulas, which can be applied to specific problems immediately, help to prevent the use of often used slip boundary conditions that are either incorrect or without theoretical basis.

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A multi-temperature hydrodynamic limit of kinetic equations is employed for the analysis of the steady shock problem in a binary mixture. Numerical results for varying parameters indicate possible occurrence of either smooth profiles or of weak solutions with one or two discontinuities.

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Starting from the Boltzmann kinetic equations for a mixture of gas molecules whose internal structure is described by a discrete set of internal energy levels, hydrodynamic equations at Euler level are deduced by a consistent hydrodynamic limit in the presence of a two-scale collision process. The fast process driving evolution is constituted by mechanical encounters between particles of the same species, whereas inter-species scattering proceeds at the macroscopic scale. The resulting multi-temperature and multi-velocity fluid-dynamic equations are briefly commented on, and some results in closed analytical form are given for special simplified situations like Maxwellian collision kernels, or monoatomic hard sphere gases.

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