Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2511.14612 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918208272859136 |
|---|---|
| author | Höfer, Richard M. Mecherbet, A. Schubert, R. |
| author_facet | Höfer, Richard M. Mecherbet, A. Schubert, R. |
| contents | We consider a microscopic model of spherical particles with inertia in a Stokes flow. As the particle number grows to infinity and their size goes to zero we derive the monokinetic Vlasov-Stokes equations as mean-field limit. We do this under the assumption that the particles have initial velocities given by a Lipschitz velocity profile and prove the mean-field limit for times of the order of the inverse Lipschitz constant. Notably this is not a perturbative result. In particular, we do not require the inertia of the particles to vanish in the limit. Thereby the result improves upon the perturbative derivation in [HS23] in the case of a monokinetic limit density. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14612 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derivation of the Monokinetic Vlasov-Stokes equations Höfer, Richard M. Mecherbet, A. Schubert, R. Analysis of PDEs We consider a microscopic model of spherical particles with inertia in a Stokes flow. As the particle number grows to infinity and their size goes to zero we derive the monokinetic Vlasov-Stokes equations as mean-field limit. We do this under the assumption that the particles have initial velocities given by a Lipschitz velocity profile and prove the mean-field limit for times of the order of the inverse Lipschitz constant. Notably this is not a perturbative result. In particular, we do not require the inertia of the particles to vanish in the limit. Thereby the result improves upon the perturbative derivation in [HS23] in the case of a monokinetic limit density. |
| title | Derivation of the Monokinetic Vlasov-Stokes equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.14612 |