THE ASYMPTOTICS OF COLLISION OPERATORS FOR TWO SPECIES OF PARTICLES OF DISPARATE MASSES

Abstract

We analyze the dynamics of a disparate mass binary gas or of a plasma in the homogeneous case, at various time scales, in the framework of the Boltzmann or Fokker–Planck equation. We intend to provide a rigorous foundation to the epochal relaxation phenomenon first pointed out by Grad. From general basic physical hypotheses, we derive the scaling of the equations as a function of the mass ratio of the particles, and we expand the collision operators in powers of this mass ratio. Then, Hilbert or Chapman–Enskog type expansions of the distribution functions allow us to investigate the dynamics of the mixture at various time scales, and we verify that the behavior of the obtained models is coherent with Grad's hypothesis.