It’s pretty crazy what dynamics you get from NS.. until one realise they emerge from a tiny part of the solution space of Einstein equations.. which themselves emerge at the low energy limit of sth much bigger.
Euler’s equations and NS have this pesky velocity field, which requires the fluid’s state to be well described by a velocity at each point in space (and a density and a pressure, but I think GR has no problem with those). This means that you need some kind of interaction between particles to get them to exchange energy so that they thermalize instead of staying in the collisionless regime. (In other words, if you have two blobs of fluid collide, you need them to not go right through each other.) And I don’t think that GR is dissipating on the relevant scales.
As a real-world example, the universe contains neat structures (the horsehead nebula is a somewhat famous example) that are consistent with dark matter distributions that don’t really resemble fluids.
yes you can : https://arxiv.org/abs/1211.1983
but you might need to understand it in the context of holography
in some frame you can recover non-relativistic symmetries, we got a paper on this back then, but so hardcore i only understand parts of it https://arxiv.org/abs/1205.5777
Research on the topic seems to have stalled a decade ago. Probably for a good reason.
Somewhere somehow dualities seems to relate completely different systems, that non relativistic dissipative systems happen in all generality somewhere in that mess is barely a surprise.
I mean, if one believes ER=EPR GR and quantum mechanics are just the same thing.