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Hydrodynamic description of transport in strongly correlated electron systems

We develop a hydrodynamic description of the resistivity and magnetoresistance of an electron liquid in a smooth disorder potential. This approach is valid when the electron-electron scattering length is sufficiently short. In a broad range of temperatures, the dissipation is dominated by heat fluxes in the electron fluid, and the resistivity is inversely proportional to the thermal conductivity, $κ$. This is in striking contrast with the Stokes flow, in which the resistance is independent of $κ$ and proportional to the fluid viscosity. We also identify a new hydrodynamic mechanism of spin magnetoresistance.