Joule heating and electronic Gurzhi effect in hydrodynamic differential transport in an electron liquid

We perform a differential resistance study in the hydrodynamic regime of electron liquid in GaAs/AlGaAs quantum wells. At zero magnetic field ($B$) a Lorentzian profile occurs in the nonlinear transport driven by a U-turn (ac) current loop, in (ac + dc) measurements a minimum deepens with the external dc current bias ($j_{dc}$). Our analysis shows that the observed electronic transport valley induced by $j_{dc}$ is attributed to Joule heating effect on the electron temperature ($T_{e}$) of electron liquid. Quantitatively, we demonstrate that the viscosity resistivity ($\Delta \rho$) is proportional to $T^{-2}$ and is consistent with the dc-current induced electronic Gurzhi effect in various configurations of measurement.