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The description of electron-electron interactions in transport problems isboth analytically and numerically difficult. Here we show that a much simplerdescription of electron transport in the presence of interactions can beachieved in nanoscale systems. In particular, we show that the electron flow innanoscale conductors can be described by Navier-Stokes type of equations withan effective electron viscosity, i.e., on a par with the dynamics of a viscousand compressible classical fluid. By using this hydrodynamic approach we derivethe conditions for the transition from laminar to turbulent flow in nanoscalesystems and discuss possible experimental tests of our predictions.Comment: 9 pages, 1 figure, Late

Hydrodynamic approach to transport and turbulence in nanoscale conductors