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We determine the structure of the hydrodynamics with conserved current, usingthe gauge/gravity duality of charged black-hole background. It turns out thateven in the presence of the external electromagnetic field at the boundary,bulk Einstein equation is equivalent to the boundary conservation of energymomentum tensor and that of current. As a consequence, the thermal conductivityand electric conductivity are calculated in terms of the parameters of thefundamental theory. We find that Wiedermann-Franz law hold with Lorentz number$1/e^2$

Hydrodynamics with conserved current from the gravity dual