Sharp local propagation of chaos for mean field particles with W^-1, kernels

We present two methods to obtain O (1/N²) local propagation of chaos bounds for N diffusive particles in W^-1, mean field interaction. This extends the recent finding of Lacker Probab. Math. Phys. , 4 (2): 377-432, 2023 to the case of singular interactions. The first method is based on a hierarchy of relative entropies and Fisher informations, and applies to the 2D viscous vortex model in the high temperature regime. In the second method, we work on a hierarchy of L² distances and Dirichlet energies, and derive the desired sharp estimates for the same model in short time without restrictions on the temperature.