Well-posedness and mean-field limit of discontinuous weighted dynamics via the relative entropy method
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917315921051648 |
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| author | Porat, Immanuel Ben Carrillo, José A. Holzinger, Alexandra |
| author_facet | Porat, Immanuel Ben Carrillo, José A. Holzinger, Alexandra |
| contents | We consider deterministic particle dynamics with time evolving weights and their associated Kolmogorov equation and mean-field equation. We prove existence and unique- ness for the limit PDE alongside estimates on the growth of the logarithmic gradient as well as existence of weak solutions for the Kolmogorov equation satisfying an appropriate entropy inequality. We then apply these estimates and the relative entropy method as developed in [17], in order to derive the associated equation as a mean field limit. Our results cover both interactions and influence kernels with mild regularity assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03629 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Well-posedness and mean-field limit of discontinuous weighted dynamics via the relative entropy method Porat, Immanuel Ben Carrillo, José A. Holzinger, Alexandra Analysis of PDEs We consider deterministic particle dynamics with time evolving weights and their associated Kolmogorov equation and mean-field equation. We prove existence and unique- ness for the limit PDE alongside estimates on the growth of the logarithmic gradient as well as existence of weak solutions for the Kolmogorov equation satisfying an appropriate entropy inequality. We then apply these estimates and the relative entropy method as developed in [17], in order to derive the associated equation as a mean field limit. Our results cover both interactions and influence kernels with mild regularity assumptions. |
| title | Well-posedness and mean-field limit of discontinuous weighted dynamics via the relative entropy method |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.03629 |