On the mean-field limit of Vlasov-Poisson-Fokker-Planck equations
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918025201975296 |
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| author | Chen, Li Jung, Jinwook Pickl, Peter Wang, Zhenfu |
| author_facet | Chen, Li Jung, Jinwook Pickl, Peter Wang, Zhenfu |
| contents | The derivation of effective descriptions for interacting many-body systems is an important branch of applied mathematics. We prove a propagation of chaos result for a system of $N$ particles subject to Newtonian time evolution with or without additional white noise influencing the velocities of the particles. We assume that the particles interact according to a regularized Coulomb-interaction with a regularization parameter that vanishes in the $N\to\infty$ limit. The respective effective description is the so called Vlasov-Poisson-Fokker-Planck (VPFP), respectively the Vlasov-Poisson (VP) equation in the case of no or sub-dominant white noise. To obtain our result we combine the relative entropy method from \cite{jabinWang2016} with the control on the difference between the trajectories of the true and the effective description provided in \cite{HLP20} for the VPFP case respectively in \cite{LP} for the VP case. This allows us to prove strong convergence of the marginals, i.e. convergence in $L^1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13038 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the mean-field limit of Vlasov-Poisson-Fokker-Planck equations Chen, Li Jung, Jinwook Pickl, Peter Wang, Zhenfu Mathematical Physics Analysis of PDEs The derivation of effective descriptions for interacting many-body systems is an important branch of applied mathematics. We prove a propagation of chaos result for a system of $N$ particles subject to Newtonian time evolution with or without additional white noise influencing the velocities of the particles. We assume that the particles interact according to a regularized Coulomb-interaction with a regularization parameter that vanishes in the $N\to\infty$ limit. The respective effective description is the so called Vlasov-Poisson-Fokker-Planck (VPFP), respectively the Vlasov-Poisson (VP) equation in the case of no or sub-dominant white noise. To obtain our result we combine the relative entropy method from \cite{jabinWang2016} with the control on the difference between the trajectories of the true and the effective description provided in \cite{HLP20} for the VPFP case respectively in \cite{LP} for the VP case. This allows us to prove strong convergence of the marginals, i.e. convergence in $L^1$. |
| title | On the mean-field limit of Vlasov-Poisson-Fokker-Planck equations |
| topic | Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2505.13038 |