A hydrodynamic model arising in the context of granular media

In this note, we propose a formal argument identifying the hydrodynamic limit of a Fokker-Planck model for granular media appearing in [1]. More precisely, in the limit of large background temperature and vanishing friction, this hydrodynamic limit is described by the classical system of isentropic gas dynamics with a nonstandard pressure law (specifically, the pressure is proportional to the cube root of the density). Finally, some qualitative properties of the hydrodynamic model are studied.