Cauchy Problem for the Ellipsoidal Bgk Model for Polyatomic Particles

The derivation of the celebrated Boltzmann equations relies heavily on the assumption that the gas consists of monatomic particles, which is not the case for most of the realistic gases. Efforts to derive Boltzmann type kinetic models soon confront with the difficulty that it is virtually impossible to write the pre and post collision velocities in an explicit form, since polyatomic molecules can possess arbitrarily complicated structures. In search of tractable model equation for polyatomic gases that avoids such difficulties, a BGK type model was suggested as a generalization of the ellipsoidal BGK model [2, 6, 7, 9, 32, 36]: