  In this paper we introduce a (partly) new approach for the study of
McKean-Vlasov equations, including singular interactions. This approach is
based on the relativeentropy on the path space in the spirit of our previous
works together with C. L{\'e}onard. Itis also used in a recent work of D.
Lacker.We show how it can be used to derive existence and uniqueness for some
singular diffusions, in particular linear mean field stochastic particle
systems and non linear SDE of McKean-Vlasov type, including Lp- Lq models, the
2D vortex model associated to the 2D Navier-Stokes equation, sub-Coulombic
interactions models or the Patlak-Keller-Segel model.We also show the
convergence and propagation of chaos as the number of particles grows to
infinity. This is obtained at the process level, not only at the Liouville
equation level.The paper thus contains new proofs and extensions of known
results, as well as new results.The main results are given at the end of the
Introduction.
