Recent Advances in the Theory of Kinetic Equations of Many Colliding Particles - V.I. Gerasimenko; I.V. Gapyak (Mathematics and Computer Science: Research Updates Vol. 2, 2025)
The chapter presents a novel perspective on kinetic equations for systems of many colliding particles, which are governed by a hierarchy of fundamental evolution equations for observables at the microscopic scale. For this purpose, the Boltzmann–Grad asymptotics of the non-perturbative solution to the Cauchy problem for a hierarchy of evolution equations for reduced observables of such systems is constructed. As a result, based on the collective behavior of colliding particles of observables the generalization of the Boltzmann kinetic equation is derived, and the process of propagation of initial correlations is described.