We investigate the well-posedness of following McKean-Vlasov equation in \(\mathbb {R}^d\) : \(\textrm{d} X_t=\sigma (t,X_t, \mu _{X_t})\textrm{d} W_t+b(t, X_t, \mu _{X_t}) \textrm{d} t,\) where \(\mu _{X_t}\) is the law of \(X_t\) . The existence of solutions is demonstrated when \(\sigma \) satisfies certain non-degeneracy and continuity assumptions, and when b meets some integrability conditions, and continuity requirements in the (generalized) total variation distance. Furthermore, uniqueness is established under additional continuity assumptions of a Lipschitz type.
