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

On Hydrodynamic Equations at the Limit of Infinitely Many Molecules