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Would a world be able to sustain a constant low pressure area such that there would be a constant wind from one side to the other?
Imagine that on one side of the world is a desert with some rocky mountains (presumably the source of the sand), over which lies the high pressure area. To the East is a liquid oxygen sea over which forms the low pressure area.
Note: The atmosphere is cold enough to support a liquid oxygen sea.
Yes, although I don't know about your liquid O2 sea. If the planet is tidally locked, such that one side is always facing its star while the other side is always facing away, it's clear that there'd be a pressure difference at first. Say, however, that that atmosphere is a very soluble gas in the oceans. If it's cold enough and the gravity of the planet is enough (to exert a larger pressure than the earth), it's possible that the atmosphere would dissolve to some extent in the ocean and sink. Since on the other side, the ocean is boiling and generally being really hot, liquid would have to replace it, which would probably be from the deep. You'd get, across the planet, a cycle of the oceans to the cold side on the top, to the hot on the bottom, and of the atmosphere, from the hot to the cold on all sides.
Of course, there's a simpler way, one quite similar to the prevailing winds on earth. Again, you'd need a tidally locked planet, but the only odd thing would be that the ocean/land would have to absorb much more heat than the atmosphere. Because of this, air close to the ground would heat drastically up. Assuming it's over an ocean, it'd also gain a lot of moisture. Colder air above would move downwards on the hot side to replace the heated air. Much like a tornado, the moist hot air would be trapped under the fast-moving higher cold air, and would have to move against the ground towards the cold side until it finds a place to punch through the cold air and get up high where it'd like to be. There, it'd precipitate, and, if the mechanisms for the creation of a tornado are understood at all (they aren't) would start a super-powerful vortex thunderhead, producing very strong storms near the middle of the planet. The air on the far cold side would be cooling, shrinking, possibly even freezing if it's as cold as you say it is, and generally pulling more air towards it.
I don't know if it'd be a global effect, but there'd definitely be a strong inclination for vast amounts of super-heated water vapor from the very hottest point to be causing winds on the sunny side. Anybody's guess to the intensity.
Yes, on a planet where energy comes from an external source (such as the sun), it would be possible to have a persistent difference in temperature that would cause a difference in pressure. For instance, in a cold area air condenses and falls closer to the ground, creating high pressure regions. In a hot area the opposite happens: heated air rises to form low pressure regions. This is essentially what causes prevailing winds (wikipedia link) on Earth. However, there are a lot of factors that determine the direction and strength of winds. For instance, the rotation of the Earth causes prevailing winds to flow westerly and easterly, and not north-south from the poles to the equator. Also there are many local variables to consider: breezes are formed where land meets water, and mountains also have an effect on air pressure.
Shorter answer: Yes it is possible to have regions where high or low pressure is dominant. But there are so many factors that influence wind direction that I don't think a completely constant wind is possible on a planet wide scale.
Under normal conditions the simple answer is unfortunately nope.
Longer: Eventually the pressure would equalize and the wind would stop.
However there could be something to make it work. Example would be - an anomaly teleporting air from there to somewhere else. - A tidaly locked planet possibly could have an effect like that as the one side is very cold (cold enough for liquid O2 even) while the other side is much hotter. However that would be quite generalized and would be a looping system (hot air rising in the hot half of the planet and cold air drawing into that area at the bottom whereas higher up the air would go the oposite direction)
You can justify any local pressure gradient being permanent by simply making it globally circular, like a large hurricane. (Actually, there's at least one planet in our Solar system with a permanent hurricane - Jupiter's red dot)
To make it most plausible, just make its conditions similar to those that cause a natural hurricane, but add in conditions for it not to move - maybe there's some heat source on the surface that keeps the eye stationary, and the winds always rotate around this point.
