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

Mathphys Analysis Seminar

Date: Tuesday, March 5, 2024 17:15 - 18:15
Speaker: Richard Schubert (University of Bonn)
Location: Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101)
Series: Mathematics and CS Seminar
Host: Julian Fischer

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).

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