  We show that weak convergence of point measures and $(2+\epsilon)$-moment
conditions imply hydrodynamic equations at the limit of infinitely many
interacting molecules. The conditions are satisfied whenever the solutions of
the classical equations for $N$ interacting molecules obey uniform in $N$
bounds. As an example, we show that this holds when the initial conditions are
bounded and that the molecule interaction, a certain $N$-rescaling of
potentials that include all $r^{-p}$ for $1<p$, is weak enough at the initial
time. In this case the hydrodynamic equations coincide with the macroscopic
equations of Maxwell.
