Quantitative particle approximation of nonlinear Fokker-Planck equations with singular kernel

In this work, we obtain quantitative convergence of moderately interacting particle systems towards solutions nonlinear Fokker-Planck equations with singular kernels. addition, prove the well-posedness for McKean-Vlasov SDEs involving these kernels and trajectorial propagation chaos associated systems. Our results only require very weak regularity on interaction kernel, including Biot-Savart attractive such as Riesz Keller-Segel in arbitrary dimension. This seems to be first time that are obtained Lebesgue Sobolev norms aforementioned particular, still holds (locally time) PDEs exhibiting a blow-up finite time. The proofs based semigroup approach combined fine analysis infinite-dimensional stochastic convolution integrals, also exploit limiting equation.