Using some high pressure gas (before or after combustion) as a fluid bearing.
A superconducting maglev bearing, possibly using fuel as coolant.
Any related work is also welcome.
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Yes, plenty of work has been done in that area. The best primer is probably the paper that kicked off the whole hydrostatic bearing discussion (this is what you mean by "some high pressure gas"), "Reddecliff and Vohr, 1969". A lot of work has been done since then. The French had a hydrostatic bearing test stand for the never-completed European staged combustion engine (TPX/TPTech). Pratt & Whitney wanted to replace the pump side bearing in one of the Space Shuttle turbopumps with a hydrostatic one, but nothing came of this either.
IHI, the Japanese rocket turbopump manufacturer, has released information about a turbopump that they want to sell overseas that uses hydrostatic bearings, so they are probably the furthest along. Unless of course SpaceX uses hydrostatic, but for all we know their bearings run on fairy dust.
Superconducting magnetic bearings have been studied as well.
Here are the three largest problems for these bearings: