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Pulsed high current experiments in single crystals of the high-$T_{c}$superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ in c-axis directedmagnetic field $H$ reveal that the $ab$-face resistance in the free flux flowregime is a solely logarithmic function of H, devoid of any power lawcomponent. Re-analysis of published data confirms this result and leads toempirical analytic forms for the $ab$-plane and c-axis resistivities:$\rho_{ab}\propto$ $H^{3/4}$, which does not obey the expected Bardeen-Stephenresult for free flux flow, and $\rho_{c} \propto H^{-3/4} \log^{2}H$.

Bardeen-Stephen flux flow law disobeyed in the high-$T_c$ superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$