Quantitative lower bound for solutions to the Boltzmann equation in non-convex domains
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918238628085760 |
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| author | Su, Jhe-Kuan |
| author_facet | Su, Jhe-Kuan |
| contents | In this article, we study the continuous mild solutions to the Boltzmann equation in a bounded spatial domain, under either angular cutoff assumption or non-cutoff assumption. Without assuming convexity of the spatial domain, we establish a Maxwellian lower bound in the cutoff case, and a weaker-than-Maxwellian lower bound for the non-cutoff case. This extends the results of \cite{Bri1,Bri2}, where the convexity of the domain was required. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03396 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantitative lower bound for solutions to the Boltzmann equation in non-convex domains Su, Jhe-Kuan Analysis of PDEs 35Q20 In this article, we study the continuous mild solutions to the Boltzmann equation in a bounded spatial domain, under either angular cutoff assumption or non-cutoff assumption. Without assuming convexity of the spatial domain, we establish a Maxwellian lower bound in the cutoff case, and a weaker-than-Maxwellian lower bound for the non-cutoff case. This extends the results of \cite{Bri1,Bri2}, where the convexity of the domain was required. |
| title | Quantitative lower bound for solutions to the Boltzmann equation in non-convex domains |
| topic | Analysis of PDEs 35Q20 |
| url | https://arxiv.org/abs/2505.03396 |