Abstract: Fluid-kinetic models like the Vlasov-Navier-Stokes and Vlasov-Stokes equation play an important role in the description of particulate flows and sprays, and therefore, among other applications, for atmospheric processes and climate science. The derivation of such models from more basic microscopic models is notoriously difficult due to the lack of control for individual particle trajectories. I will give an overview over recent progress in the derivation of the Vlasov-Stokes equation based on stability considerations for the mesoscopic equation in Wasserstein spaces. This is joint work with Richard Höfer (Regensburg) and Amina Mecherbet (Paris).
