The Interaction of an Infinite Number of
Eddy Flows for the Hard Spheres Model

O.O. Hukalov

B. Verkin Institute for Low Temperature Physics and Engineering of the National
Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine
E-mail: hukalov@ilt.kharkov.ua

Received February 14, 2020, revised September 1, 2020.

Abstract

In the paper, the explicit approximate solutions of the Boltzmann equation for the hard spheres model are obtained. They have the form of function series of Maxwellians with coeficient functions of a spatial coordinate and time. Sufficient conditions for minimizing the uniform-integral error between the parts of the Boltzmann equation for the constructed distribution
are obtained.

Mathematics Subject Classification 2010: 76P05, 45K05, 82C40, 35Q55 Key words: Boltzmann equation, hard spheres, eddy
ows, infinite modal distribution