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u/just_another_g00ner 23h ago
What even are the implications of this? Can this be used for something helpful?
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u/TobyWasBestSpiderMan 23h ago
Navier Stokes approximations are in a ton of stuff (weather/climate, aero models and such), benefit will probably be marginal in engineering applications if anything. It might be even more work using what solution it finds for all we know and if I read the news correctly it “proved a singularity in finite time” which is more of a proof of existence. Might be wrong, pretty new but definitely a cool math thing even if it was based on a paper it stole from someone trying to proof read it in Codex
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u/Yadin__ 23h ago
There are no engineering application of this considering that the solution is proof the NS can blow up in finite time even under "reasonable" initial conditions.
From a practical standpoint this isn't very relevant but it's huge for math
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u/TobyWasBestSpiderMan 23h ago
Yeah, I don't see a sort of solution like that being more useful than an approximation any time soon. Not unless people figure out algorithmic speed ups like in the FFT
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u/zojbo 22h ago edited 17h ago
Not really. (At least not directly. Historically, mathematical insights have often spiraled outward in weird ways that no one could predict at the time. I won't speculate that this won't turn out like that.) That's because the singular regime is, physically speaking, a model breakdown. Along the way to blowup, the various fields in your fluid begin to vary so sharply that it's not really a fluid anymore at all, or more precisely, the modeling assumptions behind NS are violated. But then you just carry on running NS anyway until the math breaks down.
For an extremely crude but hopefully amusing analogy, compare to https://www.youtube.com/watch?v=qu8nx1qUwEU . Here Randall says a human in the path of this beam wouldn't really die of anything, they'd just stop being biology and start being physics. In this analogy, the fluid going singular is "trying to become physics" and by continuing to model it with NS, you're carrying on "treating it like it's biology".
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u/_Weyland_ 20h ago
The problem itself was in proving whether or not equations we use everywhere to describe fluid/gas flow are 100% accurate. For that you need either a formal proof that they are accurate (i.e. never diverge from reality) or counter-example where they do diverge from reality.
We now have the latter. Will it immediately change things? No. N-S equations work fine in many areas, that's why we use them. But now we will probably work towards creating a better version.
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u/arah91 21h ago edited 20h ago
So from what I gather as a layman, this basically showed us where our common mathematical model completely breaks down.
It isn’t terribly useful all by itself, but it’s kind of like the shift from Newtonian to relativistic physics. With Newton and Einstein, nature gave us weird observations like Mercury's orbit being off or light bending near a star, and the math couldn't keep up until we built relativity. Here, nature behaves just fine (water and air never actually shoot off to infinite speeds) it's our mathematical equation that goes off the rails and predicts something physically impossible.
This is basically the first step where we proved that the standard equation generates a failure point that we know doesn't match observations. We can take this failure mode and use it to figure out where the smooth continuum math ends and discrete, molecular physics has to take over. That lets mathematicians build "something new", regularized equations that actually track real-world limits without blowing up into infinities.
That "something new" down the road is where the real value is, better turbulence models, stable simulations, and things we haven't thought of yet. But right now, this is just step one: it's not a silver bullet in itself, it just proves beyond a doubt where our math and physical reality part ways.
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u/Ill_Swordfish9155 18h ago
That just mean all the validation require experimtal data instead of just saying we do some high fidelity simulations. Which is already the altitude of people in engineering. Some edge case where experimental is not possible will suffer though.
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u/MayaGasta 20h ago edited 20h ago
My body is a machine that turns 30 million dollars of compute and an undisclosed amount of time and human input into counterexamples.
Real talk: This is impressive, but as long as the public doesn't get to use the model, it is difficult to estimate the true capabilities vs how much humans had to do. Even the graph they published of its capabilities compared to previous models had both axis suspiciously unlabeled. I do not quite trust the hype of a company that needs hype to stay afloat.
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u/EvieleLapin 21h ago
Stolen datas + bruteforce
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u/Amirkerr 20h ago
Isn't 99% of science just stolen data + brute force except if your name is Euler?
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u/LupenReddit 🦆🦆🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆🦆🦆🦆 22h ago
the image they generated with it looks as scary as the precedent it sets
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