  Consider the following McKean-Vlasov SDE: $$ d X_t=\sqrt{2}d
W_t+\int_{{\mathbb R}^d}K(t,X_t-y)\mu_{X_t}(dy)d t,\ \ X_0=x, $$ where
$\mu_{X_t}$ stands for the distribution of $X_t$ and $K(t,x): {\mathbb
R}_+\times{\mathbb R}^d\to{\mathbb R}^d$ is a time-dependent divergence free
vector field. Under the assumption $K\in L^q_t(\widetilde L_x^p)$ with $\frac
dp+\frac2q<2$, where $\widetilde L^p_x$ stands for the localized $L^p$-space,
we show the existence of weak solutions to the above SDE. As an application, we
provide a new proof for the existence of weak solutions to 2D-Navier-Stokes
equations with measure as initial vorticity.
