5. Mar 2024

Derivation of mean-field models for sedimenting particles with small inertia

Mathphys Analysis Seminar

Datum: 5. March 2024 | 17:15 – 18:15
Sprecher: Richard Schubert, University of Bonn
Veranstaltungsort: Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101)
Sprache: Englisch

Starting from a microscopic model for sedimenting particles, we will discuss the derivation of mesoscopic and macroscopic equations for the behaviour of their respective phase-space and number density. We will see that the resulting mean-field limits – the transport-Stokes and the Vlasov-Stokes equation – can be understood as zero and first order approximation of the microscopic dynamics in terms of strength of the inertia of the particles. I will show how the classical approach of Hauray to mean-field limits can be generalized to arbitrary Wasserstein distances and how information on the well-behaved zero-order approximation can be used to perturbatively derive a fluid-kinetic equation from microscopic dynamics. Based on joint work with Richard Hfer (Regensburg).