At low temperatures, in very clean two-dimensional samples the electron mean free path relative to collisions with impurities and phonons becomes greater than the sample width. At the same time, the mean free path relative to electron-electron collisions might be much less than the sample width. Under such conditions the electron transport should be described as a Poiseuille flow of a viscous charged fluid, and the sample resistance is defined by the viscosity coefficient. In magnetic field, such that the cyclotron period is comparable to the electron-electron scattering time, the viscosity coefficient diminishes and this provides a new mechanism for negative temperature-dependent magnetoresistance. Increase of the temperature destroys the Poiseuille flow and negative magnetoresistance due to emerging of scattering of electrons on acoustic phonons. We compare such the hydrodynamic theory of magnetotransport in two dimensions with recent experimental results obtained for 2D electrons in the high quality GaAs quantum wells.

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