Depending on the windings, single phase works. A lot of vacuum cleaners run that way.
AFAIK the magnetic lab stirrers you see use coils and induction as the egg did. What is happening is that a magnet or conductive material object (note in the video it says solid metal objects, it doesn't say magnets) is being subjected to a rotating field. The field rotates because AC through a coil makes a pulsing field, the coils combined make the field itself rotate. You can control the speed simply by controlling the AC frequency.
But also note that the field will affect the conductive vessel (probably heat it up if it can't make it spin) and I don't know how much of the power will get soaked up doing that.
Hey if your liquid has a lot of ions in it then maybe you don't need a stirrer but a stator!