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The linearized Boltzmann equation is considered to describe small spatialperturbations of the homogeneous cooling state. The corresponding macroscopicbalance equations for the density, temperature, and flow velocity are derivedfrom it as the basis for a hydrodynamic description. Hydrodynamics is definedin terms of the spectrum of the generator for the dynamics of the linearizedBoltzmann equation. The hydrodynamic eigenfunctions and eigenvalues arecalculated in the long wavelength limit. The results allow identification ofthe hydrodynamic part of the solution to the linearized Boltzmann equation.This contribution is used to calculate the fluxes in the macroscopic balanceequations, leading to the Navier-Stokes equations and associated transportcoefficients. The results agree with those obtained earlier by theChapman-Enskog method. The implications of this analysis for application ofmethods of linear response to granular fluids and derivation of Green-Kuboexpressions for transport coefficients are discussed

Linearized Boltzmann Equation and Hydrodynamics for Granular Gases