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/sci/ - Science & Math

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6378549 No.6378549[DELETED]  [Reply] [Original]

>"The Navier-Stokes equations of fluid flow, used to model ocean currents, weather patterns and other phenomena, have been dubbed one of the seven most important problems in modern mathematics."

https://www.simonsfoundation.org/quanta/20140224-a-fluid-new-path-in-grand-math-challenge/

Discuss

>> No.6378575

>>6378549
So is that two solutions?
One by Tao and one by that guy from Kazagastan

>> No.6378586

>>6378549
after reading that it seems that mathematicians somehow think that fluids are made of infinitesimal parts

>> No.6378592

>>6378586
You sound like a physicist.
Have you taken a fluid mechanics class?

>> No.6378593

what do they mean by blowing up? I don't get it

someone please explain

>> No.6378602

>>6378592
I mean, yeah right, you can use the equations, but using the kind of philosophy on them as if they are platonic objects right in themselves is total bullshit, there is no infinitesimal stuff in world

>> No.6378613

>>6378575
considering that otelbaev's proof is wrong and Tao's sort of contradicts it, no.

>> No.6378614

>>6378602
>>6378586
you're egregiously misinterpreting what is going on.

>> No.6378628

That article is unreadable trash. I've read the abstract on arxiv they link to, and it seems that the solution blows up if the nonlinear (convective) and forcing terms are averaged.

I don't understand what he means by averaged though, without diving into the paper proper, for which I feel no inclination to do so right now. I have a hunch that spectral truncation, however, is a special case of his more general case of averaging.

If I'm right, this isn't that unbelievable, but still a very interesting result. If, for example, the scales sufficiently larger than the Kolmogorov dissipation length scale are ignored, the dissipation won't be sufficient and I'm willing to believe that blow-up would happen in finite time.

>> No.6378635

>>6378628
Yes, that article is crap

>> No.6378669

>>6378586
>what are molecules

>> No.6378678

>>6378628
pls explain blow up

>> No.6378681
File: 22 KB, 400x400, 1376669261265.jpg [View same] [iqdb] [saucenao] [google]
6378681

>>6378669
>implying molecules are infinitesimally small

>> No.6378683

>>6378669
quantized and not infinitesimal

all continuum mechanics is like this, where there's an infinitesimal cube where all the forces act on.

>> No.6378697

>>6378683
What about gas?

>> No.6378704

>>6378697
Only if it's flowing, I think.
The little aerodynamics I took had continuous flows.

>> No.6378709
File: 550 KB, 163x153, 1362674305307.gif [View same] [iqdb] [saucenao] [google]
6378709

>a problem from phyisics is the most important problem in mathematics
>Mathematics is Applied Physics
top fucking lel

>> No.6378713

>>6378704
Thanks.

>> No.6378717

>>6378678
it makes boom

>> No.6378718

>>6378709
Most mechanics breakthroughs have been mathematics breakthroughs

>> No.6378729

>

“Can you make fancy patterns of water that actually have some computation power?” Tao asked. “I’m betting that fluids are complex enough to do this.”

i can already see the Headlines if it is actually true " Navier-Stokes equations solved Water proven to be sentient"

>> No.6378772

>>6378593
Not sure, but I'm guessing the solution going to infinity.

>> No.6378795

Was the USSR proof valid ?

>> No.6378802

>>6378709
No, Physics is Applied Mathematics.

>> No.6378810

>>6378678
The main result of the paper is that when you molest the nonlinearity in NS in some way, there cannot exist regular solution for <span class="math">t\in[0,\infty)[/spoiler] for certain initial data. He pushes it a little further showing that for a particular treatment of the nonlinearity and particular set of initial data, the solution goes to infinity at the origin in finite time, which is called the blow-up.

>> No.6378812

>>6378810
I see, thanks

>> No.6379929

bump

>> No.6379937

>>6378549
that's really fucking cool. Who'd thunk we might be able to build a Von Neumann machine out of water.

>>6378586
most fluid dynamicists do too

>> No.6379999

>>6378586
Fluid mechanics is a sub-topic of continuum mechanics.

>> No.6380010

>>6378802

physics is a subsection of applied maths.