We report a computer simulation of simple shear flow in order to investigate the transport properties of a two-dimensional microscopic model of a fluid. The numerical results exhibit nonlinear profiles for the fluid velocity, and the viscous resistance depends linearly on the shear rate. These experiments confirm that, in two-dimensional fluids, the Navier-Stokes equations do not exist in their usual form. We propose a phenomenological expression for the viscous part of the pressure.

• Received 17 December 1976

DOI:https://doi.org/10.1103/PhysRevA.16.720