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A general framework for the kinetic modeling of polyatomic gases

A general framework for the kinetic modelling of non-relativistic polyatomic gases is proposed,where each particle is characterized both by its velocity and by its internal state, and the Boltzmann collisionoperator involves suitably weighted integrals over the space of internal energies. The description of the internalstructure of a molecule is kept highly general, and this allows classical and semi-classical models, such asthe monoatomic gas description, the continuous internal energy structure, and the description with discreteinternal energy levels, to fit our framework. We prove the H-Theorem for the proposed kinetic equation ofBoltzmann type in this general setting, and characterize the equilibrium Maxwellian distribution and thethermodynamic number of degrees of freedom. Euler equations are derived, as zero-order approximation in asuitable asymptotic expansion. In addition, within this general framework it is possible to build up new models,highly desirable for physical applications, where rotation and vibration are precisely described. Examples ofmodels for the Hydrogen Fluoride gas are presented.