Error Estimation in the Mean-Field Limit of Kinetic Flocking Models with Local Alignments
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914764044632064 |
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| author | Wang, Jinhuan Li, Keyu Huang, Hui |
| author_facet | Wang, Jinhuan Li, Keyu Huang, Hui |
| contents | In this paper, we present an innovative particle system characterized by moderate interactions, designed to accurately approximate kinetic flocking models that incorporate singular interaction forces and local alignment mechanisms. We establish the existence of weak solutions to the corresponding flocking equations and provide an error estimate for the mean-field limit. This is achieved through the regularization of singular forces and a nonlocal approximation strategy for local alignments. We show that, by selecting the regularization and localization parameters logarithmically with respect to the number of particles, the particle system effectively approximates the mean-field equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13644 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Error Estimation in the Mean-Field Limit of Kinetic Flocking Models with Local Alignments Wang, Jinhuan Li, Keyu Huang, Hui Analysis of PDEs Mathematical Physics Dynamical Systems Probability In this paper, we present an innovative particle system characterized by moderate interactions, designed to accurately approximate kinetic flocking models that incorporate singular interaction forces and local alignment mechanisms. We establish the existence of weak solutions to the corresponding flocking equations and provide an error estimate for the mean-field limit. This is achieved through the regularization of singular forces and a nonlocal approximation strategy for local alignments. We show that, by selecting the regularization and localization parameters logarithmically with respect to the number of particles, the particle system effectively approximates the mean-field equation. |
| title | Error Estimation in the Mean-Field Limit of Kinetic Flocking Models with Local Alignments |
| topic | Analysis of PDEs Mathematical Physics Dynamical Systems Probability |
| url | https://arxiv.org/abs/2404.13644 |