Stochastic Dynamics and Hierarchy for the Boltzmann Equation with Arbitrary Differential Scattering Cross Section

  • M. Lampis
  • D. Ya. Petrina

Abstract

The stochastic dynamics for point particles that corresponds to the Boltzmann equation with arbitrary differential scattering cross section is constructed. We derive the stochastic Boltzmann hierarchy the solutions of which outside the hyperplanes of lower dimension where the point particles interact are equal to the product of one-particle correlation functions, provided that the initial correlation functions are products of one-particle correlation functions. A one-particle correlation function satisfies the Boltzmann equation. The Kac dynamics in the momentum space is obtained.
Published
25.12.2004
How to Cite
Lampis, M., and D. Y. Petrina. “Stochastic Dynamics and Hierarchy for the Boltzmann Equation With Arbitrary Differential Scattering Cross Section”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, no. 12, Dec. 2004, pp. 1629-53, https://umj.imath.kiev.ua/index.php/umj/article/view/3871.
Section
Research articles