2 5 N ov 2 01 2 Linear hydrodynamics for driven granular gases Maŕıa

Granular assemblies –made up of macroscopic solid bodies undergoing dissipative interactions– have been shown [1, 2] to frequently exhibit flows similar to those of normal fluids, and for practical purposes are often described by phenomenological hydrodynamic equations, i.e. equations for the density, flow velocity and energy density. This is so even if energy is not a conserved variable (the condition is that the energy mode be a slow variable compared to the rest of excitations). When the dynamics of the grains can be partitioned into sequences of two-body collisions, there is support both from experiments and computer simulations for the usefulness of a Kinetic Theory description. This occurs, schematically, when there are no clusters nor jamming and the system remains fluidized [3]. In the low density limit, the relevant dynamics is encoded in the one-particle distribution function, which obeys the inelastic Boltzmann equation [4, 5]. This is the starting point for many of the formal derivations of hydrodynamic equations by applying similar tools and ideas as those used in the context of ordinary fluids [6]. In the free-cooling case the study of the existence and applicability of a hydrodynamic regime is rather complete for the inelastic hard sphere (IHS) model. The Navier-Stokes equations have been derived by the Chapman-Enskog expansion [7] and also via the linearized Boltzmann equation [8–10], yielding equivalent Green-Kubo formulas for the transport coefficients [11]. The problem for arbitrary densities has also been tackled in [12, 13] applying linear response methods. Although the successful of the Navier-Stokes equations is remarkable, granular systems often require to go beyond this level of description. For these cases and close to a stationary state, a modification of the Chapman-Enskog expansion has been carried out taking into account rheological effects [14, 15].