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Viscosity of two-dimensional electrons

The hydrodynamic regime of electron transport has been recently realized in conductors with ultra-low densities of defects. Although relaxation processes in two-dimensional (2D) fluids have been studied in many theoretical works, the viscosity of the realistic Fermi gas of 2D electrons having the quadratic energy spectrum and interacting by Coulomb's law has not been reliably determined either in theory or in experiment up to now. Here we construct a theory of viscosity and thermal conductivity in such system. We compare the calculated viscosity of the 2D electron Fermi gas and the previously known viscosity of a 2D Fermi liquid with available experimental data extracted from the hydrodynamic negative magnetoresistance of the best-quality GaAs quantum wells. Based on this comparison, we argue that measurements of the temperature dependence of the viscosity can allow to trace the transition between an electron Fermi liquid and a Fermi gas.