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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| Published in | Journal of statistical physics Vol. 192; no. 6 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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New York
Springer Nature B.V
06.06.2025
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| ISSN | 1572-9613 0022-4715 1572-9613 |
| DOI | 10.1007/s10955-025-03459-0 |
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| Abstract | 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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| AbstractList | 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. |
| ArticleNumber | 77 |
| Author | Kim, Jong-in Lee, Donghyun |
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| SubjectTerms | Amplitudes Asymptotic properties Boltzmann transport equation Boundary conditions Kinetic theory Rarefied gases Stability |
| Title | On the Large Amplitude Solution of the Boltzmann equation with Large External Potential and Boundary Effects |
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