  We consider Mckean-Vlasov type stochastic differential equations with
multiplicative noise arising from the random vortex method. Such an equation
can be viewed as the mean-field limit of interacting particle systems with
singular interacting kernels such as the Biot-Savart kernel. A new estimate for
the transition probability density of diffusion processes will be formulated to
handle the singularity of the interacting kernel. The existence and uniqueness
of the weak solution of such SDEs will be established as the main result.
