An overview of recent results pertaining to the hydrodynamic description
(both Newtonian and non-Newtonian) of granular gases described by the Boltzmann
equation for inelastic Maxwell models is presented. The use of this
mathematical model allows us to get exact results for different problems.
First, the Navier--Stokes constitutive equations with explicit expressions for
the corresponding transport coefficients are derived by applying the
Chapman--Enskog method to inelastic gases. Second, the non-Newtonian
rheological properties in the uniform shear flow (USF) are obtained in the
steady state as well as in the transient unsteady regime. Next, an exact
solution for a special class of Couette flows characterized by a uniform heat
flux is worked out. This solution shares the same rheological properties as the
USF and, additionally, two generalized transport coefficients associated with
the heat flux vector can be identified. Finally, the problem of small spatial
perturbations of the USF is analyzed with a Chapman--Enskog-like method and
generalized (tensorial) transport coefficients are obtained.Comment: 40 pages, 10 figures; v2: final version published in a special issue
devoted to "Granular hydrodynamics
