  The linearized Boltzmann equation is considered to describe small spatial
perturbations of the homogeneous cooling state. The corresponding macroscopic
balance equations for the density, temperature, and flow velocity are derived
from it as the basis for a hydrodynamic description. Hydrodynamics is defined
in terms of the spectrum of the generator for the dynamics of the linearized
Boltzmann equation. The hydrodynamic eigenfunctions and eigenvalues are
calculated in the long wavelength limit. The results allow identification of
the hydrodynamic part of the solution to the linearized Boltzmann equation.
This contribution is used to calculate the fluxes in the macroscopic balance
equations, leading to the Navier-Stokes equations and associated transport
coefficients. The results agree with those obtained earlier by the
Chapman-Enskog method. The implications of this analysis for application of
methods of linear response to granular fluids and derivation of Green-Kubo
expressions for transport coefficients are discussed.
