  In this paper, by utilizing Wang's Harnack inequality with power and the
Banach fixed point theorem, the weak well-posedness for McKean-Vlasov SDEs with
integrable drift is investigated. In addition, using the decoupled method, some
regularity such as relative entropy and Sobolev's estimate of invariant
probability measure are proved. Finally, by Banach's fixed theorem, the
existence and uniqueness of invariant probability measure for symmetric
McKean-Vlasov SDEs and stochastic Hamiltonian system with integrable drifts are
obtained.
