Fisher information for solutions of the Boltzmann equation
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918134966910976 |
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| author | Imbert, Cyril |
| author_facet | Imbert, Cyril |
| contents | This note reviews a recent contribution about the Fisher information for the space-homogeneous Boltzmann equation by L. Silvestre, C. Villani and the author (arXiv, 2024). This classical functional from information theory is shown to be nonincreasing along the flow of the non-linear PDE for all physically relevant particle interactions. The proof consists in establishing a new functional inequality on the sphere of Log-Sobolev type. This new a priori estimate on solutions yields global-in-time well posedness of the equation, in particular in the case of very singular interactions, a left open question up to this work. L'information de Fisher des solutions de l'{é}quation de Boltzmann R{é}sum{é}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03045 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fisher information for solutions of the Boltzmann equation Imbert, Cyril Analysis of PDEs This note reviews a recent contribution about the Fisher information for the space-homogeneous Boltzmann equation by L. Silvestre, C. Villani and the author (arXiv, 2024). This classical functional from information theory is shown to be nonincreasing along the flow of the non-linear PDE for all physically relevant particle interactions. The proof consists in establishing a new functional inequality on the sphere of Log-Sobolev type. This new a priori estimate on solutions yields global-in-time well posedness of the equation, in particular in the case of very singular interactions, a left open question up to this work. L'information de Fisher des solutions de l'{é}quation de Boltzmann R{é}sum{é}. |
| title | Fisher information for solutions of the Boltzmann equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.03045 |