The goal of this talk is to discuss recent progress in the convergence problem in mean-field control theory.
We are interested in control problems involving a large number of (controlled) interacting particles subject to independent noises of Brownian type. When the number of particles tends to infinity, the problem simplifies into a control problem of mean-field type, set on the space of...
We consider the point-vortex system in a domain and assume the masses to be single-signed. We investigate the possibility of collapse with the boundary. We prove that such collapses are not possible in the case of the disk and of the half-plane. For general domains, we give a necessary condition for a collapse with the boundary to occur. This is joint work with M. Donati and L. Godard-Cadillac.
In this work, I will present a work in collaboration with Jonathan Luk where we prove that weak limits of solutions to Einstein vacuum equations, in some setting, converge to solutions to Einstein equations coupled to a massless Vlasov field. The proof uses the microlocal deffect measures of Tartar and Gérard, and compensated compactness.
