Contents Online
Communications in Mathematical Sciences
Volume 22 (2024)
Number 1
Energy method for the Boltzmann equation of monatomic gaseous mixtures
Pages: 137 – 166
DOI: https://dx.doi.org/10.4310/CMS.2024.v22.n1.a6
Authors
Abstract
In this paper, we present an energy method for the system of Boltzmann equations in the multicomponent mixture case, based on a micro-macro decomposition. More precisely, the perturbation of a solution to the Boltzmann equation around a global equilibrium is decomposed into the sum of a macroscopic and a microscopic part, for which we obtain a priori estimates at both lower and higher orders. These estimates are obtained under a suitable smallness assumption. The assumption can be justified a posteriori in the higher-order case, leading to the closure of the corresponding estimate.
Keywords
multicomponent gas mixture, energy method, micro-macro decomposition, conservation laws, smallness assumptions
2010 Mathematics Subject Classification
35Q20, 35Q35, 82C40
Received 13 October 2021
Received revised 30 August 2022
Accepted 9 May 2023
Published 7 December 2023