Strong convergence of propagation of chaos for mckean-vlasov sdes with singular interactions

In this work we show the strong convergence of propagation of chaos for the particle approximation of McKean-Vlasov SDEs with singular Lp-interactions as well as for the moderate interaction particle systems on the level of particle trajectories. One of the main obstacles is to establish the strong well-posedness of the SDEs for particle systems with singular interaction. To this end, we extend the results on strong well-posedness of Krylov and Rockner [Probab. Theory Related Fields, 131 (2005), pp. 154-196] to the case of mixed L\bfitp-drifts, where the heat kernel estimates play a crucial role. Moreover, when the interaction kernel is bounded measurable, we also obtain the optimal rate of strong convergence, which is partially based on Jabin and Wang's entropy method [P.-E. Jabin and Z. Wang, J. Funct. Anal., 271 (2016), pp. 3588-3627] and Zvonkin's transformation.