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Comment by eadmund | Hacker News Reader

What I got from the article is that there's a possibility of a chaotic result: it may not be possible to get computed results which are arbitrarily close to the real-world results. I was reminded a bit of the famous Lorenz system (originally for weather prediction, IIRC), which turns out to be chaotic under some conditions.

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I think it's not a chaotic result as such (as the Lorenz weather prediction models you're referencing are) - which would mean large differences in outcome from very small differences in input, but a case where multiple different outcomes can arise from identical inputs.

Right. It’s already known that NS solutions can be chaotic. It would be a big deal if they turned out to be non-unique.

> but a case where multiple different outcomes can arise from identical inputs.

If they are identical but not equal and these small differences in the input lead to large deviations in the output then that's pretty much the definition of a chaotic system.

Edit: I've just browsed through the paper in question and it actually demonstrates thar an approximate (weak) solution is not unique, which means that the exact same inputs in may have multiple weak form solutions.

"Weak" here does not mean numerical approximations. These are mathematicians so any quantitative approximation would be bounded o(1) otherwise the work would be meaningless. One should think of "weak" as in constraints, for example constraints at lower spatial resolutions (but precise).

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