General hydrodynamic equations from the linear Boltzmann equation

A derivation of hydrodynamic equations from the linearized Boltzmann equation is presented which is based upon Zwanzig' s projection operator method. This is obtained in the simple compact form of linearized Burnett equations with frequency and wavelength dependent transport coefficients, for which explicit expressions are given for well-behaved intermolecular potentials. The effects of the initial distribution function may be included, although for long times the initial state terms disappear. This disappearance of the initial state terms implies that for long times the general hydrodynamic equations and the Chapman-Enskog hydrodynamic equations agree. The latter are exact for all times for a special initial state. As an application of the theory, an expression is found for the dispersion equation for sound propagating in a gas, that holds for any well-behaved intermolecular potential.