Propagation of chaos for the homogeneous Boltzmann equation with moderately soft potentials
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908740229267456 |
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| author | Fournier, Nicolas Mischler, Stéphane |
| author_facet | Fournier, Nicolas Mischler, Stéphane |
| contents | We show that the Kac particle system converges, as the number of particles tends to infinity, to the solution of the homogeneous Boltzmann equation, in the regime of moderately soft potentials, $γ\in (-2,0)$ with the common notation. This proves the propagation of chaos. We adapt the recent work of Imbert, Silvestre and Villani, to show that the Fisher information is nonincreasing in time along solutions to the Kac master equation. This estimate allows us to control the singularity of the interaction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24065 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Propagation of chaos for the homogeneous Boltzmann equation with moderately soft potentials Fournier, Nicolas Mischler, Stéphane Analysis of PDEs Probability 82C40, 60K35, 65C05 We show that the Kac particle system converges, as the number of particles tends to infinity, to the solution of the homogeneous Boltzmann equation, in the regime of moderately soft potentials, $γ\in (-2,0)$ with the common notation. This proves the propagation of chaos. We adapt the recent work of Imbert, Silvestre and Villani, to show that the Fisher information is nonincreasing in time along solutions to the Kac master equation. This estimate allows us to control the singularity of the interaction. |
| title | Propagation of chaos for the homogeneous Boltzmann equation with moderately soft potentials |
| topic | Analysis of PDEs Probability 82C40, 60K35, 65C05 |
| url | https://arxiv.org/abs/2512.24065 |