The Goldstein-McKean model revisited

The main properties of the simplest spatially non-homogeneous kinetic equation (the Goldstein-McKean model) are briefly reviewed. The relationships with generalized and/or extended hydrodynamics are looked upon, as they result from the projection operator method, spectral analysis, and scaling. New interesting features of a broader, principial interest are highlighted in connection to the irreversible behavior of the system and to the scaling procedure. For systems with boundaries, one derives systematically the full set of hydrodynamic boundary conditions, up to any order.