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.

21 pages. arXiv admin note: text overlap with arXiv:1307.6676

References in corpus (7)

• Quantum Kinetic Evolution of Marginal Observables
• On the Integrated Form of the BBGKY Hierarchy for Hard Spheres
• On the non-Markovian Enskog Equation for Granular Gases
• The Brownian motion as the limit of a deterministic system of hard-spheres
• On Microscopic Origin of the Fokker - Planck Kinetic Evolution of Hard Spheres
• On the Boltzmann-Grad Limit for the classical hard-spheres system
• Introduction to the Theory of Evolution Equations of Quantum Many-Particle Systems

Cited by in corpus (6)

• On Semigroups of Large Particle Systems and their Scaling Asymptotic Behavior
• On Kinetic Equations Modeling Evolution of Systems in Mathematical Biology
• Advances in theory of evolution equations of many colliding particles
• Non-perturbative solutions of hierarchies of evolution equations for colliding particles
• Observables and Strong One-Sided Chaos in the Boltzmann-Grad Limit
• On Dynamics of Correlations in Quantum Many-Particle Systems