Singular McKean–Vlasov SDEs: Well-posedness, regularities and Wang’s Harnack inequality

The well-posedness and regularity estimates in initial distributions are derived for singular McKean–Vlasov SDEs, where the drift contains a locally standard integrable term and a superlinear term in the spatial variable, and is Lipschitz continuous in the distribution variable with respect to a weighted variation distance. When the superlinear term is strengthened to be Lipschitz continuous, Wang’s Harnack inequality is established. These results are new also for the classical Itô SDEs where the coefficients are distribution independent.