On kinetic models for polyatomic gases and their hydrodynamic limits

Starting from a kinetic Boltzmann or BGK description of a polyatomic gas, on the basis of a discrete structure of internal energy levels, an asymptotic Chapman-Enskog analysis is performed in the continuum limit in order to achieve consistent fluid-dynamic Navier-Stokes equations for the macroscopic fields. Among the various transport coefficients, emphasis is given to the dynamical pressure, which characterizes molecules with non-translational degrees of freedom, and which vanishes in the mono-atomic limit.