Mean-field limits for sedimentation of particles with inertia

In this talk we investigate systems of particles immersed in a fluid and subject to gravitation. The particles interact with each other through the fluid in a very implicit way. I will show how, relying on previous results for mean-field limits of inertialess particles, a mesoscopic description of particles with inertia can be derived. In particular I will point out the connection to the Transport-Stokes and Vlasov-Brinkmann equations as mean-field limits. The results rely on the approximation of the system by a system with much more explicit interaction and a detailed understanding of the involved forces in comparison to the case of a single particle. This is based on joint work with Richard Hoefer (Paris).