Finite time blowup for an averaged three-dimensional Navier-Stokes equation (2014)

v64•about 2 hours ago

This is going around due to rumors and baseless speculation on Twitter [1] right now that Anthropic has solved the Millennium problem related to Navier-Stokes [2]

[1] https://x.com/AndrewCurran_/status/2096062392442724805 for example

[2] https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existenc...

cacio-e-pepe•about 1 hour ago

relevant: https://mathstodon.xyz/@tao/117219101339291693

CSMastermind•about 2 hours ago

Lol as far as I know that post was the origin of that claim and it's clearly just a guy predicting something that will happen in the future with no information about it.

krackers•about 1 hour ago

Elliot Glazer (FrontierMath lead) traces how it snowballed over time

https://x.com/ElliotGlazer/status/2096298696438906934

Arodex•40 minutes ago

Not reading any x.com content until xcancel and nitter are back.

bee_rider•about 1 hour ago

For a second I thought they were aiming the scary proof machine at us mortals doing PDE stuff. Fortunately the speculation is just that they happen to be aiming it at a nearby mathematician type problem. Phew.

bilsbie•about 2 hours ago

If it is solved what are the applications of that? What changes?

margorczynski•about 1 hour ago

None really. It just says if the NS equations are realistic and can really model real physics or there exist some solutions that make it blow up (infinite energy). But even if that would exist (a solution that blows up) it doesn't mean it doesn't work for 99,999999% of the stuff we're interested in.

The question is basically a pure math question about PDEs.

goldenarm•about 2 hours ago

@dang please can we add a [2014] to the title ?

thomasahle•about 2 hours ago

Yes please. For a moment I thought Terrence Tao had scooped Anthropic.

tacomonstrous•about 2 hours ago

This is essentially irrelevant to the content of the post, but it's amusing to me that he casually mentions submitting to JAMS as if its acceptance were a mere formality.

gus_massa•about 1 hour ago

He has rejected papers too https://mathstodon.xyz/@tao/113721192051328193

Sharlin•21 minutes ago

> With hindsight, some of my past rejections have become amusing. With a coauthor, I once almost solved a conjecture, establishing the result with an "epsilon loss" in a key parameter. We submitted to a highly reputable journal, but it was rejected on the grounds that it did not resolve the full conjecture. So we submitted elsewhere, and the paper was accepted.

> The following year, we managed to finally prove the full conjecture without the epsilon loss, and decided to try submitting to the highly reputable journal again. This time, the paper was rejected for only being an epsilon improvement over the previous literature!

MeteorMarc•about 1 hour ago

See https://www.quantamagazine.org/theory-of-fluids-enters-the-2... if you want to know what the Navier Stokes equations are about.

immmmmm•about 1 hour ago

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.

cacio-e-pepe•about 1 hour ago

Could you expand? Curious.

amelius•about 1 hour ago

Interesting to see that they are not using the coordinate-free representation (exterior calculus, differential forms) that mathematical physicists prefer to use today.

auntienomen•19 minutes ago

Those notations are used when writing down the models, because they make clear the intrinsic geometry, the basic symmetries, etc. But they're not used so much in the study of solutions to the equations. Solutions tend to have peculiar features, tend to break underlying symmetries, etc. and there only needs to be one nasty particular solution to prove the NS conjecture wrong.

Finite time blowup for an averaged three-dimensional Navier-Stokes equation (2014)

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