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Lecture on the homogenization of Stokes-Brinkman type models and mean field limit, presented by Amina Mecherbet at the Centre International de Rencontres Mathématiques. Explore the rigorous derivation of fluid-kinetic models for suspensions, which are prevalent in nature and industry. The lecture reviews key results in this field, beginning with an introduction to microscopic and limiting equations, followed by a discussion of effective models derived from microscopic systems with fixed particle positions and velocities. Learn about asymptotic analysis when particle numbers increase while their radius decreases, leading to different limit equations depending on the scale of holes and their typical distance. The final section covers the derivation of fluid-kinetic models that account for fluid-particle interactions and particle dynamics, particularly focusing on Transport-Stokes equations and mean field limit approaches. The lecture was recorded during the thematic meeting "Kinetic theory and fluid mechanics: couplings, scalings and asymptotics" in March 2025 at CIRM in Marseille, France.
