Global well-posedness of the linearized R13 moment equations with Onsager boundary conditions
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917510234767360 |
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| author | Hu, Shuang Lin, Bo Liu, Huini Cai, Zhenning |
| author_facet | Hu, Shuang Lin, Bo Liu, Huini Cai, Zhenning |
| contents | This paper establishes the global well-posedness of the linearized regularized 13-moment (R13) equations for rarefied gas flows. We first derive an entropy inequality for the system on bounded domains subject to Onsager boundary conditions. For the steady-state problem, well-posedness is proved via the Ladyzhenskaya-Babuska-Brezzi (LBB) theorem, facilitated by novel boundary-related Korn-type inequalities. Furthermore, leveraging the Lumer-Phillips theorem, we extend these results to guarantee the global well-posedness of the time-dependent R13 equations. Our theoretical framework uniformly accommodates the models for both Maxwell and general non-Maxwell molecules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19415 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of the linearized R13 moment equations with Onsager boundary conditions Hu, Shuang Lin, Bo Liu, Huini Cai, Zhenning Analysis of PDEs 76P05, 82C40, 35Q20, 47D06 This paper establishes the global well-posedness of the linearized regularized 13-moment (R13) equations for rarefied gas flows. We first derive an entropy inequality for the system on bounded domains subject to Onsager boundary conditions. For the steady-state problem, well-posedness is proved via the Ladyzhenskaya-Babuska-Brezzi (LBB) theorem, facilitated by novel boundary-related Korn-type inequalities. Furthermore, leveraging the Lumer-Phillips theorem, we extend these results to guarantee the global well-posedness of the time-dependent R13 equations. Our theoretical framework uniformly accommodates the models for both Maxwell and general non-Maxwell molecules. |
| title | Global well-posedness of the linearized R13 moment equations with Onsager boundary conditions |
| topic | Analysis of PDEs 76P05, 82C40, 35Q20, 47D06 |
| url | https://arxiv.org/abs/2605.19415 |