  We prove the existence of a large class of dynamical solutions to the
Einstein-Euler equations that have a first post-Newtonian expansion. The
results here are based on the elliptic-hyperbolic formulation of the
Einstein-Euler equations used in \cite{Oli06}, which contains a singular
parameter $\ep = v_T/c$, where $v_T$ is a characteristic velocity associated
with the fluid and $c$ is the speed of light. As in \cite{Oli06}, energy
estimates on weighted Sobolev spaces are used to analyze the behavior of
solutions to the Einstein-Euler equations in the limit $\ep\searrow 0$, and to
demonstrate the validity of the first post-Newtonian expansion as an
approximation.

General Relativity and Quantum Cosmology