In this paper, utilizing Wangs Harnack inequality with power and the Banach fixed point theorem, the weak well-posedness for distribution dependent SDEs with integrable drift is investigated. In addition, using a trick of decoupled method, some regularity such as relative entropy and Sobolevs estimate of invariant probability measure are proved. Furthermore, by comparing two stationary Fokker-Planck-Kolmogorov equations, the existence and uniqueness of invariant probability measure for McKean-Vlasov SDEs are obtained by log-Sobolevs inequality and Banachs fixed theorem. Finally, some examples are presented.
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