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Dufty, Lee, Lutsko, Montanero, and Santos have carried out stability analysesof steady stationary shear flows. Their approach is based on the compressibleand heat conducting Navier-Stokes-Fourier model. It predicts the unstableexponential growth of long-wavelength transverse perturbations for both two-and three-dimensional fluids. We point out that the patently-stabletwo-dimensional periodic shear flows studied earlier by Petravic, Posch, andourselves contradict these predicted instabilities. The stable steady-stateshear flows are based on nonequilibrium molecular dynamics with simplethermostats maintaining nonequilibrium stationary states in two spacedimensions. The failure of the stability analyses remains unexplained.

Steady Periodic Shear Flow is Stable in Two Space Dimensions .  Nonequilibrium Molecular Dynamics vs Navier-Stokes-Fourier Stability Theory  -- A Comment on two Arxiv Contributions