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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/2503.02276 |
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| _version_ | 1866915182889926656 |
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| author | Porat, Immanuel Ben Carrillo, José A. Jabin, Pierre-Emmanuel |
| author_facet | Porat, Immanuel Ben Carrillo, José A. Jabin, Pierre-Emmanuel |
| contents | We study the mean field limit for singular dynamics with time evolving weights. Our results are an extension of the work of Serfaty \cite{duerinckx2020mean} and Bresch-Jabin-Wang \cite{bresch2019modulated}, which consider singular Coulomb flows with weights which are constant time. The inclusion of time dependent weights necessitates the commutator estimates of \cite{duerinckx2020mean,bresch2019modulated}, as well as a new functional inequality. The well-posedness of the mean field PDE and the associated system of trajectories is also proved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02276 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singular flows with time-varying weights Porat, Immanuel Ben Carrillo, José A. Jabin, Pierre-Emmanuel Analysis of PDEs We study the mean field limit for singular dynamics with time evolving weights. Our results are an extension of the work of Serfaty \cite{duerinckx2020mean} and Bresch-Jabin-Wang \cite{bresch2019modulated}, which consider singular Coulomb flows with weights which are constant time. The inclusion of time dependent weights necessitates the commutator estimates of \cite{duerinckx2020mean,bresch2019modulated}, as well as a new functional inequality. The well-posedness of the mean field PDE and the associated system of trajectories is also proved. |
| title | Singular flows with time-varying weights |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.02276 |