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We consider hydrodynamic electron transport in the Hall-bar geometry. Thetheory is developed for systems with non-Galilean-invariant electron liquids.We show that inhomogeneity of the electron density induced by long-rangedisorder and gating leads to mixing between the hydrodynamic transport mode andtransport relative to the electron liquid. For graphene systems near chargeneutrality, these effects lead to strong coupling of the hydrodynamic flow tocharge transport. As a result, the effective electrical conductivity of thesystem may significantly exceed the intrinsic conductivity of the electronliquid. We obtain analytic expressions for the thermoelectric transportcoefficients of the system as a function of density in the full crossoverregion between clean and disorder-dominated regimes.

Hydrodynamic electron transport in graphene Hall-bar devices