Derivation of the Monokinetic Vlasov-Stokes equations
Analysis of PDEs
2025-11-19 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2511.14612,
title = {Derivation of the Monokinetic Vlasov-Stokes equations},
author = {Richard M. Höfer and A. Mecherbet and R. Schubert},
journal= {arXiv preprint arXiv:2511.14612},
year = {2025}
}
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21 pages