On the Large Amplitude Solution of the Boltzmann equation with Large External Potential and Boundary Effects

The Boltzmann equation is a fundamental equation in kinetic theory that describes the motion of rarefied gases. In this study, we examine the Boltzmann equation within a C1 bounded domain, subject to a large external potential Φ(x) and diffuse reflection boundary conditions. Initially, we prove the...

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Bibliographic Details
Published inJournal of statistical physics Vol. 192; no. 6
Main Authors Kim, Jong-in, Lee, Donghyun
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 06.06.2025
Subjects
Amplitudes
Asymptotic properties
Boltzmann transport equation
Boundary conditions
Kinetic theory
Rarefied gases
Stability
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ISSN1572-9613
0022-4715
1572-9613
DOI10.1007/s10955-025-03459-0

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Summary:The Boltzmann equation is a fundamental equation in kinetic theory that describes the motion of rarefied gases. In this study, we examine the Boltzmann equation within a C1 bounded domain, subject to a large external potential Φ(x) and diffuse reflection boundary conditions. Initially, we prove the asymptotic stability of small perturbations near the local Maxwellian μE(x,v). Subsequently, we demonstrate the asymptotic stability of large amplitude solutions with initial data that is arbitrarily large in (weighted) L∞, but sufficiently small in the sense of relative entropy. Specifically, we extend the results for large amplitude solutions of the Boltzmann equation (with or without external potential) [10, 11–12, 23] to scenarios involving significant external potentials [19, 28] under diffuse reflection boundary conditions.
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ISSN:1572-9613
0022-4715
1572-9613
DOI:10.1007/s10955-025-03459-0