Kinetic Theory with Fluctuations: Strong Well-Posedness of the Vlasov-Fokker-Planck-Dean-Kawasaki System
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913171367788544 |
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| author | Hao, Zimo Wu, Zhengyan Zimmer, Johannes |
| author_facet | Hao, Zimo Wu, Zhengyan Zimmer, Johannes |
| contents | The strong well-posedness of the Vlasov-Fokker-Planck-Dean-Kawasaki (VFPDK) equation with correlated noise is established. This equation can be interpreted as the fluctuating mean-field limit of second-order Newtonian particle systems, combining kinetic theory with stochastic fluctuations. It includes bounded nonlocal interactions and a diffusion coefficient exhibiting a square-root structure. Key challenges stem from the complexity of the kinetic operator and the irregularity introduced by the conservative noise with square-root-type coefficients. The proof relies on a novel combination of kinetic semigroup estimates and the framework of renormalized kinetic solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10194 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kinetic Theory with Fluctuations: Strong Well-Posedness of the Vlasov-Fokker-Planck-Dean-Kawasaki System Hao, Zimo Wu, Zhengyan Zimmer, Johannes Probability Analysis of PDEs The strong well-posedness of the Vlasov-Fokker-Planck-Dean-Kawasaki (VFPDK) equation with correlated noise is established. This equation can be interpreted as the fluctuating mean-field limit of second-order Newtonian particle systems, combining kinetic theory with stochastic fluctuations. It includes bounded nonlocal interactions and a diffusion coefficient exhibiting a square-root structure. Key challenges stem from the complexity of the kinetic operator and the irregularity introduced by the conservative noise with square-root-type coefficients. The proof relies on a novel combination of kinetic semigroup estimates and the framework of renormalized kinetic solutions. |
| title | Kinetic Theory with Fluctuations: Strong Well-Posedness of the Vlasov-Fokker-Planck-Dean-Kawasaki System |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2511.10194 |