  The stability of idealized shear flow at long wavelengths is studied in
detail. A hydrodynamic analysis at the level of the Navier-Stokes equation for
small shear rates is given to identify the origin and universality of an
instability at any finite shear rate for sufficiently long wavelength
perturbations. The analysis is extended to larger shear rates using a low
density model kinetic equation. Direct Monte Carlo Simulation of this equation
is computed with a hydrodynamic description including non Newtonian rheological
effects. The hydrodynamic description of the instability is in good agreement
with the direct Monte Carlo simulation for $t < 50t_0$, where $t_0$ is the mean
free time. Longer time simulations up to $2000t_0$ are used to identify the
asymptotic state as a spatially non-uniform quasi-stationary state. Finally,
preliminary results from molecular dynamics simulation showing the instability
are presented and discussed.
