  We establish a new local well-posedness result in the space of finite Borel
measures for mild solutions of the parabolic-elliptic Patlak-Keller-Segel (PKS)
model of chemotactic aggregation in two dimensions. Our result only requires
that the initial measure satisfy the necessary assumption $\max_{x \in
\Real^2}\mu(\set{x}) < 8\pi$. This work improves the small-data results of
Biler and the existence results of Senba and Suzuki. Our work is based on that
of Gallagher and Gallay, who prove the uniqueness and log-Lipschitz continuity
of the solution map for the 2D Navier-Stokes equations (NSE) with
measure-valued initial vorticity. We refine their techniques and present an
alternative version of their proof which yields existence, uniqueness and
\emph{Lipschitz} continuity of the solution maps of both PKS and NSE. Many
steps are more difficult for PKS than for NSE, particularly on the level of the
linear estimates related to the self-similar spreading solutions.
