Analysis of the Relaxation Process Using Nonrelativistic Kinetic Equation

We study the linearized kinetic equation of relaxation model proposed by Bhatnagar, Gross and Krook [P. L. Bhatnagar, E. P. Gross and M. Krook, Phys. Rev. 94 (1954), 511] (also called BGK model) and solve the dispersion relation. Using the solution of the dispersion relation, we analyze the relaxation of the macroscopic mode and kinetic mode. Since the BGK model is not based on the expansion in the mean free path in contrast to the Chapman-Enskog expansion, the solution can describe the accurate relaxation of initial disturbance with any wavelength. This nonrelativistic analysis gives suggestions for our next work on the relativistic analysis of relaxation.