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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.17821 |
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| _version_ | 1866908556404457472 |
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| author | Feistl-Held, Manuela Pickl, Peter |
| author_facet | Feistl-Held, Manuela Pickl, Peter |
| contents | We present a probabilistic proof of the mean-field limit and propagation of chaos of a classical N-particle system in two dimensions with Coulomb interaction force of the form $f^N(q)=\pm\frac{q}{|q|^2}$ and $N$-dependent cut-off at $|q|>N^{-2}$. In particular, for typical initial data, we show convergence of the Newtonian trajectories to the characteristics of the Vlasov-Poisson system. The proof is based on a Gronwall estimate for the maximal distance between the exact microscopic dynamics and the approximate mean-field dynamics. Thus our result leads to a derivation of the Vlasov-Poisson equation from the microscopic $N$-particle dynamics with force term arbitrary close to the physically relevant Coulomb force. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17821 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the mean-field limit for the Vlasov-Poisson system in two dimensions Feistl-Held, Manuela Pickl, Peter Analysis of PDEs Mathematical Physics Dynamical Systems Classical Physics 70-10, 82Dxx G.3 We present a probabilistic proof of the mean-field limit and propagation of chaos of a classical N-particle system in two dimensions with Coulomb interaction force of the form $f^N(q)=\pm\frac{q}{|q|^2}$ and $N$-dependent cut-off at $|q|>N^{-2}$. In particular, for typical initial data, we show convergence of the Newtonian trajectories to the characteristics of the Vlasov-Poisson system. The proof is based on a Gronwall estimate for the maximal distance between the exact microscopic dynamics and the approximate mean-field dynamics. Thus our result leads to a derivation of the Vlasov-Poisson equation from the microscopic $N$-particle dynamics with force term arbitrary close to the physically relevant Coulomb force. |
| title | On the mean-field limit for the Vlasov-Poisson system in two dimensions |
| topic | Analysis of PDEs Mathematical Physics Dynamical Systems Classical Physics 70-10, 82Dxx G.3 |
| url | https://arxiv.org/abs/2509.17821 |