In a plasma at rest, the electrostatic potential around a point charge obeys the well-known Debye shielding law. Modifications, for the ease of a flowing plasma, have been studied in the limiting cases of either long or short distances for subsonic and hypersonic velocities. Only recently this was extended to include all distances, restricted to a two-dimensional case. However, neither of these modifications includes the ionic motions. In this paper, we derive general expressions for the electrostatic potential which are valid for all distances and flow velocities in one-, two- and three-dimensional cases. This is done first with unperturbed ions, and then for the case where ionic motions, which are seen to be important for mesothermic flow velocities, are included. In both cases, the results are discussed and illustrated.