New explicit approximate solution of the Boltzmann equation in the case of the hard sphere model

Authors

  • O. Hukalov B. I. Verkin Institute of Low Temperature Physics and Technology, Kharkiv and Kharkiv National University named after V. N. Karazin https://orcid.org/0000-0003-2099-5036
  • V. Gordevskyy B. I. Verkin Institute of Low Temperature Physics and Technology, Kharkiv and Kharkiv National University named after V. N. Karazin

DOI:

https://doi.org/10.3842/umzh.v77i8.9164

Keywords:

The Boltzmann equation, hard spheres, the uniform-integral error, ''accelerating-packing'' motion

Abstract

UDC 517.9

We construct an approximate solution to the nonlinear kinetic Boltzmann equation for the case of hard-sphere model. It has the form of an infinite sum of some Maxwellian modes with coefficient functions of the spatial coordinate and time. We establish sufficient conditions for the coefficient functions and  hydrodynamic parameters appearing in the distribution and allowing us to make the analyzed deviation arbitrarily small.

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Published

11.09.2025

Issue

Vol. 77 No. 8 (2025)

Section

Research articles

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Copyright (c) 2025 Олексій Гукалов, Вячеслав Гордевський

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Hukalov, O., and V. Gordevskyy. “New Explicit Approximate Solution of the Boltzmann Equation in the Case of the Hard Sphere Model”. Ukrains’kyi Matematychnyi Zhurnal, vol. 77, no. 8, Sept. 2025, pp. 503–520, https://doi.org/10.3842/umzh.v77i8.9164.