Global renormalized solutions to Boltzmann systems modeling mixture gases of monatomic and polyatomic species
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915723291394048 |
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| author | Luo, Yi-Long Nie, Jing-Xin |
| author_facet | Luo, Yi-Long Nie, Jing-Xin |
| contents | Inspired by DiPerna-Lions' work \cite{Diperna-Lions}, we study the renormalized solutions to the large-data Cauchy problem of the Boltzmann systems modeling mixture gases of monatomic and polyatomic species, in which the distribution functions $f_α$ characterized the polyatomic species contain the continuous internal energy variable $I \in \mathbb{R}_+$. We first construct the smooth approximated problem and establish the corresponding uniform and physically natural bounds. Then, by employing the averaged velocity (-internal energy) lemma, we can show that the weak $L^1$ limit of the approximated solution is exactly a renormalized solution what we required. Moreover, we also justify that the constructed renormalized solution subjects to the entropy inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07480 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global renormalized solutions to Boltzmann systems modeling mixture gases of monatomic and polyatomic species Luo, Yi-Long Nie, Jing-Xin Analysis of PDEs Inspired by DiPerna-Lions' work \cite{Diperna-Lions}, we study the renormalized solutions to the large-data Cauchy problem of the Boltzmann systems modeling mixture gases of monatomic and polyatomic species, in which the distribution functions $f_α$ characterized the polyatomic species contain the continuous internal energy variable $I \in \mathbb{R}_+$. We first construct the smooth approximated problem and establish the corresponding uniform and physically natural bounds. Then, by employing the averaged velocity (-internal energy) lemma, we can show that the weak $L^1$ limit of the approximated solution is exactly a renormalized solution what we required. Moreover, we also justify that the constructed renormalized solution subjects to the entropy inequality. |
| title | Global renormalized solutions to Boltzmann systems modeling mixture gases of monatomic and polyatomic species |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.07480 |