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 superlinear spatial variable, is Lipchitz continuous distribution variable with respect to weighted variation distance. When strengthened be Lipschitz continuous, Wang’s Harnack inequality established. These results new also classical Itô SDEs coefficients independent.