A global simulation for the auroral electrojet on Jupiter is presented. The required sequence of models was computed using JIM (the Jovian Ionospheric Model), a time-dependent, three-dimensional model for the thermosphere and ionosphere of Jupiter, and an a priori model for the planet's ionospheric electric field. We describe the plasma dynamics in the model by considering ion and electron motions at pressure levels less than 2 µbar, lying above Jupiter's dynamo region, and including the region of maximum energy deposition by auroral particles. By considering the motions of the neutral species being `dragged' by the electrojet, we quantify the electrodynamic coupling between the neutral thermosphere and the auroral ionosphere. Two distinct altitude regions evolve in the model simulations, distinguished by different thermospheric flow patterns. Higher-altitude regions are subject to gas dynamic flow, while lower-altitude regions are strongly influenced by electrodynamic flow, associated with the transfer of momentum from the electrojet to the neutral gas. The electrojet models provide a basis for physical interpretation of current observational detections of ion motions in the Jovian auroral regions; as well as a means of optimizing future observations, in order to make similar detections.