
Solution claimed for Navier-Stokes equations, one of the millennium problems - ColinWright
http://www.inform.kz/eng/article/2619922
======
ColinWright
It appears that the same comment is being made over and over again, so it's
worth putting a brief summary of the answers:

No, this is not yet peer reviewed. This is breaking news, and it's not had
time to be assessed by experts in the fields, or even people who are
tangentially acquainted.

However, unlike P vs NP, this problem does not have a long history of a
"proof" per day by cranks, and a paper every year or so by established
mathematicians. It's unusual to see a paper claiming anything substantial
about this problem.

If you're interested, here's a link to the actual paper:

[http://www.math.kz/images/journal/2013-4/Otelbaev_N-
S_21_12_...](http://www.math.kz/images/journal/2013-4/Otelbaev_N-
S_21_12_2013.pdf)

It's in Russian. If you can read Russian, and are acquainted with the math
involved, then feedback would be most welcome. In the meantime this might be
the solution, it might be an ultimately flawed but useful advance, or it might
be nonsense.

It is, however, news.

 _Added in edit: This comment looks useful, but is not encouraging:_

[https://news.ycombinator.com/item?id=7042941](https://news.ycombinator.com/item?id=7042941)

 _Having said that, if it has been solved by someone who is primarily in a
teaching (as opposed to research) post, then it 's plausible that they would
spend some time (12 pages? Hmm) setting up the problem and notation._

~~~
georgecmu
In the paper he mentions that he's been interested in pursuing this problem
since 1980. A list of his selected publication is available here:
[http://www.mathnet.ru/php/person.phtml?personid=29899&option...](http://www.mathnet.ru/php/person.phtml?personid=29899&option_lang=eng)

His paper may contain errors, but he's not a crank.

------
calhoun137
A long time ago, I started working on an approach that never panned out,
attempting to prove that such solutions could not exist. I will briefly
mention it here in case anyone would like to comment or continue the strategy.

In [1] I learned that it is known that certain differential equations
associated with embedding manifolds in R^n possess no smooth solutions. And in
[2] I asked if it was possible that the Navier-Stokes equations were of this
nature, since if this was the case it would create a clear path towards a
negative solution. There was no definitive answer given, but the community (of
mathSE) did seem to agree that it would turn it this is not the case.

[1] [http://math.stackexchange.com/questions/8586/what-is-an-
exam...](http://math.stackexchange.com/questions/8586/what-is-an-example-of-a-
second-order-differential-equation-for-which-it-is-known) (See Willie Wong's
answer)

[2] [http://math.stackexchange.com/questions/9085/manifold-
interp...](http://math.stackexchange.com/questions/9085/manifold-
interpretation-of-navier-stokes-equations)

------
danabramov
The PDF (in Russian):

[http://www.math.kz/images/journal/2013-4/Otelbaev_N-
S_21_12_...](http://www.math.kz/images/journal/2013-4/Otelbaev_N-
S_21_12_2013.pdf)

There is a small summary at the end in English, although it only seems to
cover the problem:

[http://i.imgur.com/fVqVBiE.png](http://i.imgur.com/fVqVBiE.png)

------
mabbo
I'll believe it when I see the prize get awarded. Until then, I'll file this
beside that guy who writes a 'solution' to P=NP every month on arxiv.org.

~~~
sheetjs
I wish people who submit links to HN would think before doing so.

~~~
dominotw
Would you rather see more of 'why I dont eat lunch at my desk' stories?

~~~
sheetjs
If this article had a link to the actual document "Existence of the strong
solution of Navier-Stokes equations", then we could have an actual discussion
about the mathematics.

Incidentally, the google results for "Existence of the strong solution of
Navier-Stokes equations" are the article and some links which point to this HN
post: [http://i.imgur.com/2pf8kMa.png](http://i.imgur.com/2pf8kMa.png)

~~~
ColinWright
It doesn't take much effort to find the actual article. Here you go:

[http://www.math.kz/images/journal/2013-4/Otelbaev_N-
S_21_12_...](http://www.math.kz/images/journal/2013-4/Otelbaev_N-
S_21_12_2013.pdf)

------
jawns
Link to CMI's Millennium Problems:

[http://www.claymath.org/millennium-
problems](http://www.claymath.org/millennium-problems)

Relevant summary:

"Navier–Stokes Equation: This is the equation which governs the flow of fluids
such as water and air. However, there is no proof for the most basic questions
one can ask: do solutions exist, and are they unique? Why ask for a proof?
Because a proof gives not only certitude, but also understanding."

~~~
calhoun137
There are already a large number of solutions to Navier-Stokes that are known.
The millennium problem asks to prove existence or non-existence of _smooth_
(infinitely differentiable) solutions that are valid for _all time_ See pg 2,
here:
[http://www.claymath.org/sites/default/files/navierstokes.pdf](http://www.claymath.org/sites/default/files/navierstokes.pdf)

------
dborg
At this rate they'll all be solved by mid-century. Weren't these supposed to
last us like a millenium or something?

~~~
ZenoArrow
"Weren't these supposed to last us like a millenium or something?" Why would
you think that?

~~~
dborg
I was making a joke about the name...

~~~
ZenoArrow
Ah okay, guess I misunderstood.

------
Keyframe
I wonder, if true, how it will change CFD. That is, will it change at all.

~~~
afroncioni
Well, if it is true, then it could indeed change CFD. Imagine that the
computational stencil can solve itself using a closed-form equation. A strong
solution implies that you don't have to form matrices to couple the linearised
equations.

------
f137
Well, just to put it in some context. The paper was published in the Eurasian
Mathematical Journal, of which the author is the editor-in-chief.

------
calhoun137
According to this article, he claims to have found a strong solution. My
prediction was/is that the types of solutions asked for by the millennium
problem were not going to exist, so my first instinct is to not believe this,
but clearly that is not a good reason. So, at the risk of being wrong, I will
make the following not so bold prediction: there is a critical mistake
somewhere in the paper and the approach will ultimately not pan out.

~~~
sp332
The prize is awarded either way. You have to prove that a solution exists _or_
doesn't exist. [http://www.claymath.org/millennium-problems/rules-
millennium...](http://www.claymath.org/millennium-problems/rules-millennium-
prizes) _In the case of the P versus NP problem and the Navier-Stokes problem,
the SAB will consider the award of the Millennium Prize for deciding the
question in either direction._

~~~
ckozlowski
Precisely. In the case of the NP-hard example I presented below, the
researcher (who's name eludes me) attempted to prove that a solution did not
exist.

From a computer science perspective, this would be favorable, as a solution
for NP-hard would render a lot of crypto useless overnight. =P

~~~
umanwizard
Why do people keep repeating this notion? P doesn't mean fast or even
tractable within the expected lifetime of the universe. "Polynomial time
algorithms are fast" is an extremely vague statement for intuition, and not
actually true except if you define carefully what you mean (that is, that they
are faster as n->+inf...)

If crypto relies on some algorithms that are O(n^100000000000) where n is key
length, I'm not very worried.

------
kken
Kinda strange, I cannot find the manuscript and not even his homepage
([http://otelbaev.com](http://otelbaev.com)) is updated.

Wouldn't one expect this to be reported either after a successful peer review
or after publication of a preprint?

His citation index is not very convincing either
[http://scholar.google.com/citations?user=CU2sU8YAAAAJ](http://scholar.google.com/citations?user=CU2sU8YAAAAJ)

Smells fishy.

~~~
mythealias
Basing opinion on citation index is like saying if this person is not widely
cited he is likely to be wrong. From what I know, it is common for researchers
in US and EU to cite each other. However work from say China or other
Asian/African nations is not cited as often.

I know many (well-established) professors who don't bother updating their
webpage. In fact some of them wouldn't have eve bothered keeping a webpage had
it not been for the courses.

That said I will take this news with a grain of salt because it is not an easy
problem and definitely needs a through review.

~~~
kken
>Basing opinion on citation index is like saying if this person is not widely
cited he is likely to be wrong.

No, it does not say that.

Having published for 40 years with only very few citations means that his
works were either irrelevant or only found extremely limited circulation. Both
makes the claims less trustworthy. However, on the other hand, Perelman...

~~~
auntienomen
Perelman wasn't an academic nobody. He was a Miller fellow at Berkeley, and
had visiting positions at the Courant Institute and Stony Brook. When he left
the academic system, he had job offers at Princeton and Stanford.

TL;DR People who work on geometry knew Perelman pretty well.

------
mywolfson
I have started to translate the paper so that English speakers can explore it.
I've only had time for the abstract, introduction, and main result statement,
but that already gives an important part of the picture. Any further
contributions are welcome.
[https://github.com/myw/navier_stokes_translate](https://github.com/myw/navier_stokes_translate)

------
num3ric
Any implications for computational fluid dynamics methods?

------
julie1
Remember physics does not work like maths: physic is the art of solving an
equation without calculating it.

Usual tricks are: \- reducing one degrees of liberty per symmetry (this can
involve creating abstract symmetries); \- making 2 coupled dimensions
uncoupled by introducing perturbations that tends to 0; \- making weired
assumption on the form of the solution (definite, continuous, and derivable in
all points) because if you are not in quantum mechanics, your solution rarely
accepts discrete change of values);

Thus I am intuitively thinking the navier stockes solution cannot be found by
a mathematician. I was pretty much expecting an approximation of the solution
by a physicist because it requires the kind of free spirit accepting to make
hypothesis that normally makes a mathematician have an heart attack.

The physical solutions tends to be a subset of the mathematical equations.
Physicists tends to discard solutions that would involve the world exploding
every time a fluid is flowing (I don't know why).

Am I the only one that noticed that Maxwell Equations are looking like a
weired simplified sets of Navier Stokes equation in a case of a very weired
perfect gaz? (viscosity = 0, compressibility = 0, and a weired twist about
vortex (rotational seems related to vortex), and at the opposite of NS a time
dependency on two fluids (E and B) that are kind of independent but dual (rot
and div meaning seem to be swapped in their role for B and E), and a ...
weired kind of coupling on B and E over time?)

DivE = is expressing the compressibility RotE is expressing the vorticity of E
...

And the funniest of Maxwell law is that at the end they seem to be
relativistic (c is appearing in the equation of propagation and is the limit)

Man, I so would like to see a geometrical interpretation of the maxwell
equation as a dual space coupling, so we can use intuition instead of math to
solve it.

I so wish I had time to study this... I would really try to solve NS by first
solving Maxwell. :)

I am betting the solution as for relativity is involving at least one non
euclidean geometry. In fact since it involves "time" I could call it not a
geometry (wich is time agnostic) but a dynametry :)

The equivalents of formal axiom of geometry describing formal solutions of
canonical "dynamic space" that would be attractors of stable solutions and
rules to transform them.

~~~
VladRussian2
>Am I the only one that noticed that Maxwell Equations are looking like a
weired simplified sets of Navier Stokes equation in a case of a very weired
perfect gaz? (viscosity = 0,

Faraday's original approach was the "flow" of the field ( that was later
mathematized by Maxwell).

------
chm
It's funny how seeing this paper written in Russian makes me want to learn the
language. The Anglosphere is only part of the story!

------
apples2apples
Clay Mathematics Page still lists it as unsolved. I know of dozens of
"solutions" that have not been accepted. Do we know if this is just submitted
or actually accepted by the scientific community.

------
bubka
Translation to English has been started
([https://github.com/myw/navier_stokes_translate](https://github.com/myw/navier_stokes_translate))

------
wanda
Does his proof involve Hilbert & Fourier spaces? How about Hilbert-Schmidt
superoperators?

~~~
julie1
Fourier would be acceptable if and only if there were only linear solution to
the problem. No?

My reasoning is the following : NS also describes non linear behaviour
(turbulent flows that are sensitive to the initial condition thus that may
result in solutions that looks like white noise).

Linear algebrae can't be used to solve non linear phenomena and thus if a
solution is looking like temporal noise, I guess the fourier of the time serie
would also would like a solution with a density of probability that would be
constant on all spectrum of frequencies that are compatible with the physics
(no energy travel faster then the speed of light, hence, there is an upper
limit to the frequency).

Am I stupid to expect non linear algebrae involved like Liouville theorem ?

------
SpaceRaccoon
great success! now we can calculate optimal trajectory of nuclear missile bomb
to destroy assholes uzbekistan

------
rvac
Wawawiwa!

~~~
aerolite
Very nice.

