Time evolution equations for hydrodynamic variables with arbitrary initial data

We prescribe an alternative procedure for arriving at the time evolution equations for hydrodynamic local variables such as density, velocity fields, and kinetic energy using a time evolution equation of the single-particle distribution. It is suggested that when applied to various combinations of pair-potential between monoatoms, geometry and initial data, the prescription will have wide applications in hydrodynamics, including solutions of the Navier–Stokes equation.