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March 9, 2014 1:49 PM   Subscribe

Finite time blowup for an averaged three-dimensional Navier-Stokes equation - "[Terence Tao] has shown that in an alternative abstract universe closely related to the one described by the Navier-Stokes equations, it is possible for a body of fluid to form a sort of computer, which can build a self-replicating fluid robot that, like the Cat in the Hat, keeps transferring its energy to smaller and smaller copies of itself until the fluid 'blows up.' " [1,2,3] (previously)
posted by kliuless (15 comments total) 19 users marked this as a favorite

 
“The real ocean doesn’t spontaneously blow up, of course”
posted by jepler at 2:04 PM on March 9 [2 favorites]


Klarreich is really good, consistently turning in longform pieces on actually important mathematical research developments that are accessible but also give some sense of the real issues involved.
posted by escabeche at 2:09 PM on March 9 [1 favorite]


Don't ask me what voom is, I'll never know. But boy let me tell you, it does clean up snow.
posted by newton at 2:53 PM on March 9 [2 favorites]


This... would mean ice-9 is actually a self-replicating fluid robot that BSODs.
posted by ardgedee at 2:56 PM on March 9 [1 favorite]


The reliance on a nearby universe reminds me somewhat of the description of Mochizuki's approach to the abc problem I read about in a New Scientist article in which you were quoted, escabeche.

Perhaps we could have a sequence of toy universes with the Navier-Stokes universe as an unincluded limit point, a la Skolem.
posted by jamjam at 3:25 PM on March 9


The reliance on a nearby universe reminds me somewhat of the description of Mochizuki's approach to the abc problem I read about in a New Scientist article in which you were quoted, escabeche.

Not the same kind of "universe," though you could argue for a sort of analogistic similarity.

What Terry's doing is saying, "there's a program for proving Navier-Stokes doesn't blow up using properties A, B, and C of Navier-Stokes, which seem to make it awfully hard for singularities to develop; but here I display a differential equation which also satisfies A, B, and C, and which I've cleverly set up to generate singularities, which shows that any proof of non-blow-up for Navier Stokes is going to have to use more than A, B, and C."
posted by escabeche at 4:28 PM on March 9 [12 favorites]


The paper on arXiv.
posted by benito.strauss at 5:32 PM on March 9 [1 favorite]


Terence Tao of the University of California, Los Angeles, has proposed a new approach to understanding the solutions to the Navier-Stokes equations of fluid flow.

I love that the guy trying to solve the mystery of the flow is called Tao.
posted by billiebee at 6:34 PM on March 9 [3 favorites]


fwiw, keith devlin on navier-stokes (also btw A Brief Synopsis of The Millennium Problems; oh and Terence Tao: What is good mathematics? ;)
posted by kliuless at 7:52 PM on March 9 [1 favorite]


“The real ocean doesn’t spontaneously blow up, of course”

Yet, anyway.
posted by pjern at 6:26 AM on March 10


Terence Tao is ridiculously talented. I know him mostly for his work on compressive sensing, but he seems to have done very well-received work in all kind of different, disparate areas of math.
posted by Maecenas at 7:48 AM on March 10


but he seems to have done very well-received work in all kind of different, disparate areas of math.

This is the textbook definition of understatement.
posted by Elementary Penguin at 8:17 AM on March 10 [1 favorite]


While this may be a long way from a purely fluid-mechanical blowup, the real ocean did spontaneously emit some blobs of protoplasm that came back after a few million years and blew things up quite spectacularly, e.g. the Bikini Atoll.
posted by mubba at 8:29 AM on March 10


I love that the guy trying to solve the mystery of the flow is called Tao.

Yeah, I was pretty stoked about that too.
posted by radwolf76 at 9:22 PM on March 11 [1 favorite]


The real ocean doesn’t spontaneously blow up, of course

Possibly because the real ocean is not an isotropic continuous fluid but is actually composed of discrete molecules? So we can't keep going to smaller and smaller cats....
posted by phliar at 4:43 PM on March 12


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