On the large amplitude solution of the Boltzmann equation with large external potential and boundary effects
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913883982135296 |
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| author | Kim, Jong-in Lee, Donghyun |
| author_facet | Kim, Jong-in Lee, Donghyun |
| contents | 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 $C^1$ 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 $μ_E (x,v)$. Subsequently, we demonstrate the asymptotic stability of large amplitude solutions with initial data that is arbitrarily large in (weighted) $L^\infty$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16814 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the large amplitude solution of the Boltzmann equation with large external potential and boundary effects Kim, Jong-in Lee, Donghyun Analysis of PDEs 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 $C^1$ 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 $μ_E (x,v)$. Subsequently, we demonstrate the asymptotic stability of large amplitude solutions with initial data that is arbitrarily large in (weighted) $L^\infty$, 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. |
| title | On the large amplitude solution of the Boltzmann equation with large external potential and boundary effects |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.16814 |