Linear and nonlinear hydrodynamics of low-friction adsorbed systems

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 $\sigma$ is set equal to zero, the Navier-Stokes equations obtain, but for large $\sigma$, Fick's law and diffusive behavior for the density emerge. It is found that for $\sigma$ 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.