Speaker
Description
We consider the N spherical particles suspended in a Stokes flow in R³. The particles satisfy a no-slip boundary condition and are subject to constant gravity with a mean-field scaling. The dynamics of the particles is modeled by Newton's laws. We discuss the rigorous derivation of the Vlasov-Stokes equation in the limit N →∞. The main difficulty arises from the implicit and singular particle interaction which we can only well approximate by an effective interaction as long as have sufficient control on the inter particle distances. Currently, we are able to achieve this in 1) the monokinetic setting and 2) when the inertia of the particles vanishes as N →∞. The proof is based on an adaptation of an approach of Hauray-based on 2-Wasserstein distances, and a stability estimates for the Vlasov-Stokes equation that builds on the energy dissipation of the system.
