V.I. Gerasimenko (Institute of Mathematics, Kyiv)
I.V. Gapyak (National Taras Shevchenko University of Kyiv)

The Boltzmann–Grad asymptotic behavior of marginal observables in collisional kinetic theory

Abstract:
We develop a rigorous formalism for the description of kinetic evolution of a hard sphere system in the Boltzmann–Grad scaling limit within the framework of marginal observables. For initial states specified by means of a one-particle distribution function the relationship of the Boltzmann–Grad asymptotic behavior of a nonperturbative solution of the Cauchy problem of the dual BBGKY hierarchy for marginal observables of hard spheres with a solution of the Boltzmann kinetic equation is established. One of the advantages of such an approach to the derivation of the Boltzmann equation is an opportunity to construct the kinetic equation, involving correlations at initial time, in particular, that can characterize the condensed states. Moreover, it gives to describe the propagation of initial correlations in the Boltzmann–Grad scaling limit.