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A model is proposed which interpolates between the diffusive picture for particles adsorbed on a surface and the full hydrodynamics of a compressible fluid. The model is the Navier-Stokes equations modified by a friction term. When the friction parameter is set equal to zero, the Navier-Stokes equations obtain, but for large, Fick's law and diffusive behavior for the density emerge. It is found that for small enough, the dynamic structure factor should display sound peaks in a certain wave-number range. It is also shown that the infrared divergences that signal the breakdown of hydrodynamics for two-dimensional fluids are regulated by the frinction term. The possibility of observing the sound modes and the nonlinear corrections to the transport coefficients is discussed.
Ramaswamy et al. (Wed,) studied this question.