Time correlation function of the shear stress in sheared particle systems

The long-time behaviors of the time correlation function $C_\eta(t)$ of the shear stress for three-dimensional sheared fluids are investigated theoretically. It is found that there are the cross-overs in $C_\eta(t)$ from $t^{-3/2}$ to $t^{-2}$ for sheared fluids of elastic particles without any thermostat, and from $t^{-3/2}$ to $t^{-5/2}$ for isothermal sheared fluids including granular fluids.