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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.02854 |
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| _version_ | 1866911770975666176 |
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| author | Choi, Young-Pil Fagioli, Simone Iorio, Valeria |
| author_facet | Choi, Young-Pil Fagioli, Simone Iorio, Valeria |
| contents | We investigate various versions of multi-dimensional systems involving many species, modeling aggregation phenomena through nonlocal interaction terms. We establish a rigorous connection between kinetic and macroscopic descriptions by considering the small-inertia limit at the kinetic level. The results are proven either under smoothness assumptions on all interaction kernels or under singular assumptions for \emph{self-interaction} potentials. Utilizing different techniques in the two cases, we demonstrate the existence of a solution to the kinetic system, provide uniform estimates with respect to the inertia parameter, and show convergence towards the corresponding macroscopic system as the inertia approaches zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02854 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Small inertia limit for coupled kinetic swarming models Choi, Young-Pil Fagioli, Simone Iorio, Valeria Analysis of PDEs 35A01, 35A21, 82C40, 35Q70 We investigate various versions of multi-dimensional systems involving many species, modeling aggregation phenomena through nonlocal interaction terms. We establish a rigorous connection between kinetic and macroscopic descriptions by considering the small-inertia limit at the kinetic level. The results are proven either under smoothness assumptions on all interaction kernels or under singular assumptions for \emph{self-interaction} potentials. Utilizing different techniques in the two cases, we demonstrate the existence of a solution to the kinetic system, provide uniform estimates with respect to the inertia parameter, and show convergence towards the corresponding macroscopic system as the inertia approaches zero. |
| title | Small inertia limit for coupled kinetic swarming models |
| topic | Analysis of PDEs 35A01, 35A21, 82C40, 35Q70 |
| url | https://arxiv.org/abs/2402.02854 |