Two-particle kinetic equation: method and exact solution

Abstract

In the paper (Saveliev, in: AIP conference proceedings, vol 1333, p 134, 2011), the kinetic equation for two-particle distribution function was obtained by making use of exactly the same physical assumptions as Ludwig Boltzmann did. Instead of the collision integral, there are the linear scattering operator and the chaos projector in the right part of this equation. The Boltzmann equation follows from this two-particle equation without any additional assumptions after a simple integration. The article presents the method of generalized functions and considers the properties of the obtained exact solution for the two-particle kinetic equation for Maxwell's molecules, which is an intermediate asymptotics for problems of spatial homogeneous relaxation. After reducing the two-particle distribution function to a one-particle distribution function, the solution is reduced to the well-known Bobylev-Krook-Wu (BKW) mode.