Macroscopic estimate of the linear Boltzmann and Landau equations with Specular reflection boundary
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909062159925248 |
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| author | Chen, Hongxu Kim, Chanwoo |
| author_facet | Chen, Hongxu Kim, Chanwoo |
| contents | In this short note, we prove an $L^6$-control of the macroscopic part of the linear Boltzmann and Landau equations. This result is an extension of the test function method of Esposito-Guo-Kim-Marra~\cite{EGKM}\cite{EGKM2} to the specular reflection boundary condition, in which we crucially used the Korn's inequality \cite{DV2} and the system of symmetric Poisson equations \cite{Bernou}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11693 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Macroscopic estimate of the linear Boltzmann and Landau equations with Specular reflection boundary Chen, Hongxu Kim, Chanwoo Analysis of PDEs In this short note, we prove an $L^6$-control of the macroscopic part of the linear Boltzmann and Landau equations. This result is an extension of the test function method of Esposito-Guo-Kim-Marra~\cite{EGKM}\cite{EGKM2} to the specular reflection boundary condition, in which we crucially used the Korn's inequality \cite{DV2} and the system of symmetric Poisson equations \cite{Bernou}. |
| title | Macroscopic estimate of the linear Boltzmann and Landau equations with Specular reflection boundary |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2307.11693 |