Approaches to Derivation of the Boltzmann Equation with Hard Sphere Collisions

Abstract: In the paper the possible approaches to the rigorous derivation of the Boltzmann kinetic equation with hard sphere collisions from underlying dynamics are considered. In particular, a formalism for the description of the evolution of infinitely many hard spheres within the framework of marginal observables in the Boltzmann--Grad scaling limit is developed. Also we give consideration to one more approach of the description of the kinetic evolution of hard spheres in terms of a one-particle distribution function governed by the non-Markovian generalization of the Enskog equation and the Boltzmann--Grad asymptotic behavior of its non-perturbative solution is established.