Kinetic equations for smooth granular systems II. The non-homogeneous gas

In the present work we derive hydrodynamic equations for the infinite, rarified, smooth, non-homogeneous spherical granular gas. The long-time behavior of these equations is analyzed and we show that the diffusive modes become negligible compared to the propagating modes of the system. This suggests that a mechanism of clustering is responsible for the relative freezing of the diffusive modes.