Companion papers in this series present (1) the role of equatorial E region postsunset ionosphere, (2) the origin of horizontal plasma shear flow in the postsunset equatorial ionosphere (this paper), (3) the Coloured Bubbles experiments results, and (4) computer simulations of artificial initiation of plasma density depletions (bubbles) in the equatorial ionosphere. Within this paper, equations describing the time evolution of the equatorial ionosphere are developed using flux tube integrated and flux weighted quantities which model the chemistry, dynamics, and electrodynamics of the equatorial ionosphere. The resulting two-dimensional set of equations can be used to investigate equatorial electric fields neglecting small-scale phenomena (&lgr;<1 km). An immediate result derived from the integrated current equations is an equation describing the physics of the shear in the horizontal flow of the equatorial plasma during the evening hours. The profile of the horizontal flow has three important contributing terms relating to the neutral wind dynamo, Hall conduction, and the equatorial electrojet current divergence. Using a one-dimensional model of the velocity shear equation and the integrated ionospheric transport equations, a time history of the development of the shear feature during the postsunset hours is presented. The one-dimensional model results are compared to the velocity shear measurements from the Coloured Bubbles experiments. ¿ American Geophysical Union 1992