Burnett equations for the ellipsoidal statistical BGK model

In order to discuss the agreement of the ellipsoidal statistical BGK (ES-BGK) model with the Boltzmann equation, Burnett equations are computed by means of the second-order Chapman-Enskog expansion of the ES-BGK model. It is found that the Burnett equations for the ES-BGK model with the correct Prandtl number are identical to the Burnett equations for the Boltzmann equation for Maxwell molecules (fifth-order power potentials). However, for other types of particle interaction, the Boltzmann Burnett equations cannot be reproduced from the ES-BGK model.