How could the air be stopped from falling off of a flat world?
Imagine you had a flat earth scenario, in which the world is essentially a giant disc floating in space (I know that in reality any such world would be pulled into a sphere by gravity, but for the sake of the question assume that gravity just pulls "down" instead of towards the center of mass). Now direct your attention to the edge of the disc: without something to stop them, all of the air is just going to pour over it, leaving the planet incapable of supporting life.
What measures could be taken to prevent that from happening? One thing I've thought of is placing giant mountains along the entire rim, tall enough to hold in the whole atmosphere, but I'm interested in whether there are any other passive solutions that would work in the real world (ie, no magic or teleportation).
EDIT:
A recurring question seems to be "why wouldn't the Earth and everything on it be falling at an equal speed?" Let's hand-wave it away by saying that the Earth is already at the "bottom" of the universe, and so cannot fall any further. Things on the top, however, can still slide, jump, or fall off and then descend through space until they reach the "bottom" too. Arbitrary, yes, but I think it allows us to focus more on the question itself: how do we keep the atmosphere on top of the flat surface, besides adding huge mountains around the edges?
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1 answer
The whole universe could be filled with air. That would also explain why the world isn't just in free-fall (and thus effectively gravitation-free): It is going at the limit speed where air resistance equals gravitational pull. Of course it would still not explain why the air doesn't fall as well.
Note that the effect for an inhabitant of the world would be that beyond the border of the world there's a strong upwards wind. Probably eddies would cause an outwards wind near the edge of the world.
Edit:
In response to your edit of the question:
If the universe has a bottom, and the flat earth rests on it, the filled-with-air universe gets even more plausible. Especially, there's no need for it to be completely filled with air; the air just sits on the bottom of the universe, and the flat earth is inside that universal atmosphere. For an observer on the flat earth, the only difference between that and the eternal-falling earth model is the absence of the off-earth wind (and the absence of needing to hand-wave away why the air is not falling as well; it's not falling because there's a bottom).
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