Linear and nonlinear viscous flow in two-dimensional fluids

We report on molecular dynamics simulations of shear viscosity eta of a dense two-dimensional fluid as a function of the shear rate gamma. We find an analytic dependence of eta on gamma, and do not find any evidence whatsoever of divergence in the Green-Kubo (GK) value that would be caused by the well-known longtime tail for the shear-stress autocorrelation function, as predicted by the mode-coupling theory. In accordance with the linear response theory, the GK value of eta agrees remarkably well with nonequilibrium values at small shear rates.