Non-Newtonian two-dimensional electron fluid in magnetic field

We develop a theory of the non-Newtonian regime of non-linear hydrodynamic magnetotransport of a two-dimensional (2D) viscous electron fluid controlled by the local Joule heating. In this mechanism, the electron shear viscosity in magnetic field becomes a non-monotonic function of the gradient of the hydrodynamic velocity due to the flow-induced increase of the electron temperature. We derive and solve the corresponding non-linear hydrodynamic equations for a velocity profile in a Poiseuille-like flow geometry. We demonstrate that the calculated magnetoresistance of such flow well explains the differential magnetoresistance observed for 2D electrons in various samples of ultra-high-quality GaAs quantum wells at high currents. We conclude that the non-linear regime of 2D electron fluid flows is such systems is realized via formation of a 2D non-Newtonian electron fluid, related to non-linearity in viscosity, but not via convective ``kinematic-induced'' effects, as it takes place in ordinary uncharged fluids.