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The inelastic Boltzmann equation for a granular gas is applied to spatiallyinhomogeneous states close to the uniform shear flow. A normal solution isobtained via a Chapman-Enskog-like expansion around a local shear flowdistribution. The heat and momentum fluxes are determined to first order in thedeviations of the hydrodynamic field gradients from their values in thereference state. The corresponding transport coefficients are determined from aset of coupled linear integral equations which are approximately solved byusing a kinetic model of the Boltzmann equation. The main new ingredient inthis expansion is that the reference state $f^{(0)}$ (zeroth-orderapproximation) retains all the hydrodynamic orders in the shear rate. Inaddition, since the collisional cooling cannot be compensated locally forviscous heating, the distribution $f^{(0)}$ depends on time through itsdependence on temperature. This means that in general, for a given degree ofinelasticity, the complete nonlinear dependence of the transport coefficientson the shear rate requires the analysis of the {\em unsteady} hydrodynamicbehavior. To simplify the analysis, the steady state conditions have beenconsidered here in order to perform a linear stability analysis of thehydrodynamic equations with respect to the uniform shear flow state. Conditionsfor instabilities at long wavelengths are identified and discussed.Comment: 7 figures; previous stability analysis modifie

Transport coefficients for an inelastic gas around uniform shear flow: Linear stability analysis