Applicability of the hydrodynamic description of classical fluids

We investigate using numerical simulations the domain of applicability of the hydrodynamic description of classical fluids at and near equilibrium. We find this to be independent of the degree of many-body correlations in the system; the range r_c of the microscopic interactions completely determines the maximum wavenumber k_{max} at which the hydrodynamic description is applicable by k_{max}r_c ~ 0.43. For the important special case of the Coulomb potential of infinite range, we show that the ordinary hydrodynamic description is never valid.