Talk:Navier–Stokes existence and smoothness/Archive 4

This is an archive of past discussions about Navier–Stokes existence and smoothness. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Archive 1

Archive 2

Archive 3

Archive 4

Archive 5

EJDE paper

Gavia Immer mentioned the P vs NP problem further up the page. I notice per [1] item #45 that besides this recent work on Navier-Stokes, Jorma Jormakka also solved P vs NP in 2008:

"[Not equal]: In September 2008, Jorma Jormakka proved that P is not equal to NP by showing that the subset sum problem cannot be solved in polynomial time. His paper "On the existence of polynomial-time algorithms to the subset sum problem" is available at http://arxiv.org/abs/0809.4935."

The arxiv paper about subset-sum was last revised on August 4, 2010 and is, per the author, "still believed to be correct". These two Clay Millenium problems are in very different areas of mathematics, so Jorma Jormakka is obviously a highly versatile researcher. However, a proposed solution to a famous problem like NS has to be taken as an extraordinary claim (WP:REDFLAG). It would be helpful to have secondary sources regarding the EJDE paper before we include it in the article, at least with the current description. Is there an entry in Math Reviews about it? Has Fefferman said anything? 69.111.192.233 (talk) 06:57, 22 November 2010 (UTC)

I rewrote the section for neutrality and length, but would support removing it unless secondary sources appear. 69.111.192.233 (talk) 10:02, 22 November 2010 (UTC)

Dear Gavia immer, The text that was inserted by the previous person was neither correct and nor neutral. Especially the claims that Terence Tao would have discussed the problem and shown errors in it are false. Tao neither discussed nor found errors. Also, incorrect was the claim that the proof is based on ambiguous language in the problem statement. The EJDE article is based on clear statements, actually lack of necessary conditions, in the problem statement. The EJDE article has been checked by many competent mathematicians. You are wellcome to show it incorrect if you can. It is in Wiki so that those who can show it incorrect will do so before the two years from publication of the article have passed. It is a published peer.reviewed journal article, and the highest type of references used in Wiki are published peer-reviewed journal articles. It can be referred to without any statements by Fefferman. There are other versatile researchers, no reason to make suggestive hints. Maybe the commentor would like to take a look also e.g. at arxiv:1011.3962 and the articles in google.scholar before concluding anything of my competence. I rewrote the text to be neutral and correct, and made the argument clearer. Jorma Jormakka —Preceding unsigned comment added by 88.114.52.63 (talk) 07:48, 23 November 2010 (UTC)

Prof. Jormakka, I'd ask you to stop editing the article, per Wikipedia's guideline on conflict of interest, WP:COI. Let uninvolved editors write the section. I felt that I gave a neutral explanation of the ambiguous language issue, but I'm open to suggestions about alternate phrasing. That Tao discussed the issue with you is an obvious fact. It's true that he didn't continue the discussion for as long as you'd have liked him to, and I didn't mention that in the paragraph, but I can add something about it if you want. It's also obviously true that he described what he saw as problems in your paper. Of course his opinion that there are problems is not guaranteed to be correct, but I think my wording made it sufficiently clear that it was his opinion. My judgment is that the opinion of a specialist like Tao on a subject like this is a significant point of view which should therefore be included under our neutrality policy. I felt ok using his blog as source since it was first introduced into the article by you yourself.

Also,it's not accurate to say that published papers are the highest form of reference in Wikipedia. They are acceptable for most things but extraordinary claims (which this is) require extraordinary proof, which in this case means secondary sources. We just went through something like this in the P vs NP article, where someone was trying to add a reference to a P=NP "proof" that got into an Indian journal somehow. You (or someone) also mentioned Penny Smith. You might remember that her Navier-Stokes paper had to be withdrawn because one of the earlier theorems it relied on turned out to be wrong despite having been in a journal (the error got past the referees somehow). And to not belabor the obvious, if getting a paper published settled an issue, the Clay Institute would issue its million dollar prizes immediately on publication instead of having a two year waiting period.

Of course I'm still in favor of removing the section completely. The version I wrote was intended as a compromise, mentioning the paper in what I hoped a neutral way with due weight. But really, the significance of the paper to the topic can only be established by secondary sources, and the closest thing we have to that is Tao's comments, which are quite unfavorable. 69.111.192.233 (talk) 08:43, 23 November 2010 (UTC)

I removed the section.[2] I'm ok with the idea of putting something back, but it should be shorter and more neutral than what I removed. I'm mostly ok with its description of Tao's comment but would want to adjust the phrasing a bit more. 69.111.192.233 (talk) 08:49, 23 November 2010 (UTC)

Fine, as you removed it, put there the text you want but write it correctly. The reasons there should be a reference are 1) Somebody else, not me, wanted to put it there originally. I think if somebody wanted it there, there should be good reasons not to include it. 2) It is highly relevant to the millennium prize problem description because it contains the only solution that have been published in a peer-reviewed reputable journal and has not be found incorrect, unlike Deolalikar's unpublished and refuted paper, or Smith's withdrawn paper. The paper as it is has now lasted over 2.5 years while many mathematicians have read it. Tao's fast written comment does not change anything since his comments are wrong. 3) The article shows two important problems in the problem statement. At least previously, have not checked now, there was an error also on the Wiki page. It claimed that the periodic problem is stated in torus. It is not, it is stated in R^4 with periodic velocity and force. Jorma Jormakka —Preceding unsigned comment added by 88.114.52.63 (talk) 10:49, 23 November 2010 (UTC)

I see, the first mention of Tao was in this edit which I guess was by someone other than you. I'm sorry about the confusion. If you want to suggest some short neutral wording to reference the paper, please do so here on the talk page. In particular it should state somehow that the problem solved was not the expected one (I can accept that my own attempt to explain that wasn't so good). Alternatively I can ask at Wikiproject Math for someone from there to suggest wording.

If you are seeking technical discussion of the paper's contents, Wikipedia is not the place for that. You might instead open a Math Overflow thread (www.mathoverflow.net). There are a lot of good mathematicians there (including Tao) and you are sure to get well-informed comments. 69.111.192.233 (talk) 01:07, 24 November 2010 (UTC)

Weak solution, better formulation?

The article states:

"The mathematician Jean Leray in 1934 proved the existence of so called weak solutions to the Navier–Stokes equations, satisfying the equations in mean value, not pointwise.[3]"

The phrase "in mean value" is misleading to the layperson.

Some physicists for example might not even consider that a "solution" which tests correctly against all (rapidly falling) smooth functions, in particular smooth L2-approximations of Dirac delta distributions, could be less than a strong solution.

Explaining the meaning and also the shortcomings of the 'weak solution' concept isn't easy. If someone can do this concisely, please change that part of the article. Otherwise I would rather remove the last part of the sentence and instead leave it at something like:

"The mathematician Jean Leray in 1934 proved the existence of so called weak solutions to the Navier–Stokes equations. See 'weak solution' for further explanation." — Preceding unsigned comment added by 85.179.12.135 (talk) 18:18, 26 July 2011 (UTC)

broken foot note

There is a note "[6, p. 294]" but there is no reference number 6 for this to refer to. RJFJR (talk) 19:00, 9 September 2011 (UTC) ([6] Heinbockel J.H. (2001) Introduction to Tensor Calculus and Continuum Mechanics. Trafford Publishing , ISBN: 978-1553691334 ). — Preceding unsigned comment added by 188.163.17.146 (talk) 17:40, 16 September 2011 (UTC)

eq

Long discussion this page has. Isn`t a 32kb limit for main article pages? W.org should apply some trimm-article-bots. Hello, allow me to point my problem <quote> 4. There exists a constant $E\in (0,\infty )$ such that $\int _{\mathbb {T} ^{3}}\vert \mathbf {v} (x,t)\vert ^{2}dx<E$ for all $t\geq 0\,.$ </quote>

allow e be yours constant, then find modulus of integrative.

v=340m/s
dx=0.1m, where upperscript in integrantor is 10m;

if you do the integration then you get

ky=integ.(340^2*0.1)|₁^10m = 1 156 000 - 115 600 = 1 040 400 m^3/s^2.

if a e constant equal ky then, unit value which is? value?

e_l = ky/e = 1 040 400/2.78 m^3/s^2 = 374 244.6 m^3/s^2

if arguement

ky < e

isnot true, then

ky > e it is true.

my question is next: may it be out there both inequality substraction in T-space, meaning:

374 244 m^3/s^2 - 2.78 = ?

the problem may have been copied to the article page with a mistake, or it is inappropiatly at w.org. 86.121.67.182 (talk) 18:42, 22 September 2011 (UTC)Paul

solution is

$E\in (0,\infty )\cdot$ metre

About the problem

Considering that

to solve a Navier–Stokes equation is equivalent with to approximately solve the problem using classical molecular dynamics

and that

to solve the problem using classical molecular dynamics is equivalent with to approximately solve the problem using first principle molecular dynamics,

is not it trivial that the problem has only weak solutions, if we accept the uncertainty principle?

CES1596 (talk) 17:01, 10 February 2011 (UTC)

On the contrary, if we assume an infinite hierarchy of matter as proved by René Descartes in Principia philosophiae mathematically, we can take the limit of the hierarchy, which means that the uncertainty converges to zero.

CES1596 (talk) 22:36, 6 July 2013 (UTC)

Another complete solution?

I've heard that it has resolved, but the original paper only in Russian. Why in Russian? I wish to read it in Russian though a little hard.

Отелбаев, Мухтарбай (2013). "Существование сильного решения уравнения Навье - Стокса" (PDF). Математический журнал (in Russian). 13 (4 (50)): 5–104. ISSN 1682-0525.

abstruct: В работе дано решение шестой проблемы тысячелетия (The Millennium Problem): доказаны существование и единственность сильного решения трёхмерной задачи Навье — Стокса с периодическими краевыми условиями по пространственным переменным.--Enyokoyama (talk) 12:19, 11 January 2014 (UTC)

Because this author writes in Russian, many original mathematical works were written in Russian, French, German. An English version of abstract you will find at the last page of PDF file. Otelbayev (Otelbaev, [3]) is quite famous mathematician and his claim looks to be a serious. However, anonymous user undid my revision, so let's wait for secondary sources before inserting this claim to the article. Anyway, a verification of Otelbayev's result will take a long time and we cannot say that the problem has been solved, Bezik (talk) 14:29, 11 January 2014 (UTC)

Some enthusiasts began translating this paper into English here: https://github.com/myw/navier_stokes_translate . However, only a few first pages are ready by now. Dmitry Fomin (talk) 20:04, 17 January 2014 (UTC)

Dear Dmitry Fomin and Bezik. Very much thanks for your explanations! May I ask you an elementary questions? When the boundary condition is periodic, will not the turbulence problem occur? In the paper the author said:

the coefficient of viscosity, ν, is taken to be 1, without loss of generality.

At least in the case of R^3 the turbulence problem should be very big aspect of this problem. Or have someone already been proved the statement?　If so, the condition (C) with periodic b.c. would be very different from the condition (A) with non periodic b.c..--Enyokoyama (talk) 02:48, 18 January 2014 (UTC)

One can apply scaling in order to normalize the viscosity 1 -- this has nothing to with whether one considers solutions on R^3 or on a periodic domain. Viscosity != 1/Re and so setting viscosity to be 1 does not exclude turbulence from occurring. 78.49.232.159 (talk) 13:51, 19 January 2014 (UTC)

There is some discussion of this paper at Tao's blog, starting here. Tao himself comments[4] and points to some other analyis written in Spanish. Overall the paper seems to be getting a fairly subdued reception in the math world, so the article should mention it but not overemphasize it. 50.0.121.102 (talk) 21:53, 23 January 2014 (UTC)

Thanks, everybody! Of course, I had already T. Tao's article and I'm speaking. It is also important to formulate the turbulence problem mathematically in the both cases, periodic and not periodic, which is notoriously difficult.--Enyokoyama (talk) 23:14, 23 January 2014 (UTC)

The mention of this claimed solution should be removed. I am aware that the New Scientist (unwisely) wrote an article regarding this claim, however no mathematician worth his salt believes this claim, indeed a counterexample to this claim has already been shown: http://math.stackexchange.com/questions/634890/has-prof-otelbaev-shown-existence-of-strong-solutions-for-navier-stokes-equatio http://dxdy.ru/topic80156-90.html (Russian)

There is a reason why the big news organisations did not pick this story up, and I am sure they were advised against it (as it seems New Scientist likely was by Fefferman). 2001:638:902:2001:214:BFF:FE81:48CE (talk) 12:48, 27 January 2014 (UTC)

I tend to agree with this. Some serious mistakes have apparently been found in the paper. 70.36.142.114 (talk) 02:56, 9 February 2014 (UTC)

Protection from self-promotion

This edit request has been answered. Set the |answered= or |ans= parameter to no to reactivate your request.

I am not exactly sure of Wikipedia's policy on protecting wikis, however it may be advantageous to restrict the number of so called 'solutions' being constantly added/removed from the wiki (see above). Unfortunately, the prestige attached to solving this problem seems to attract numerous well meaning but ultimately incorrect attempts -- some of which are published in journals lacking proper peer review (see above). Serious attempts are normally quickly retracted, however there are also a vocal class of not so serious attempts from individuals who relentlessly push their 'solutions' on well known members of the field and places like Wikipedia. A plausible solution should be easily identifiable by acceptance from experts in the field -- none of the above 'solutions' meet this basic criteria. — Preceding unsigned comment added by 85.181.119.143 (talk • contribs) 10:17, 6 July 2014 (UTC)

Not done: requests for increases to the page protection level should be made at Wikipedia:Requests for page protection. Sam Sailor ^Sing 11:12, 6 July 2014 (UTC)

Yet another solution proposed?

46.203.12.80 wrote an paper as an extern link. But there is no explanation about it and I do not know whether paper has been reviewed, then I'll copy it the bellow in this notes field.

Navier –Stokes First Exact Transformation.

--Enyokoyama (talk) 15:12, 8 November 2013 (UTC)

Universal Journal of Applied Mathematics is an international peer-reviewed journal that publishes original and high-quality research papers in all areas of Applied Mathematics . As an important academic exchange platform, scientists and researchers can know the most up-to-date academic trends and seek valuable primary sources for reference. http://www.hrpub.org/journals/jour_archive.php?id=26

Year!　Thanks! I have already comfirm that Universal Journal of Applied Mathematics is an peer-reviewed journal. I've read it and seen that you don't solve the Millennium problem but you claim that the NSF Exact Transformation of the classical method would give a nice hint for it. I might expect more explanations in another article on wikipedia or so on.--Enyokoyama (talk) 08:32, 9 November 2013 (UTC)

“more explanations in another article on wikipedia or so on” read the author site http://www.continuum-paradoxes.narod.ru/

To Slawekb

Why you have ignored a comment --Enyokoyama (talk) and have removed an external link Navier –Stokes First Exact Transformation. ? — Preceding unsigned comment added by 46.203.110.78 (talk) 11:16, 13 November 2013 (UTC)

This link simply seems to be self-promotion. It is not published in a reputable journal and so any claims of peer-review seem dubious at best. Indeed since it misstates the Navier-Stokes equation (no advective term) one could only consider it a joke. As such it should be removed. 2001:638:902:2001:214:BFF:FE81:48CE (talk) 15:44, 10 February 2014 (UTC)

Terence Tao in 18 March, 2007 announced http://terrytao.wordpress.com/2007/03/18/why-global-regularity-for-navier-stokes-is-hard/ three possible strategies if one wants to solve the full Millennium Prize problem for the 3-dimensional Navier-Stokes equation. Strategy 1 “Solve the Navier-Stokes equation exactly and explicitly (or at least transform this equation exactly and explicitly to a simpler equation)” is used in works:

The author of these works Alexandr Kozachok has offered (in February 2008 - Internet, in November 2013 and February 2014 - INTERNATIONAL journal) two exact transformations to the simpler equations. Universal Journal of Applied Mathematics is an INTERNATIONAL peer-reviewed journal. Why these links should be removed? I think, the removal makes sense when serious errors are found. Otherwise this removal contradicts to the Wiki rules.94.153.74.179 (talk) 10:13, 14 February 2014 (UTC)

Being an international journal just involves basically have a webpage and spamming a bunch of second rate academics to accept editorial roles. This is not a proper peer-review journal of note as is demonstrated by the fact it accepted this paper which misstates the Navier-Stokes equations itself. This is the exactly the kind of journal you would expect to accept randomly generated papers. I cannot imagine a more serious error than getting the equations themselves wrong! 203.217.26.35 (talk) 12:54, 15 February 2014 (UTC)

These short papers (3 and 4 pages!) written in a way that gives insight to mathematicians (even of "second rate”), physicists, engineers, students who may not be experts in this important topic. Therefore you can find any serious mistakes, if you are a mathematician even of "second rate” or student. Please, try to do it (for example, here http://math.stackexchange.com/ )! I hope for your courage!

In mathematics the emotions are unsuitable proofs!

Please read carefully the comments. The Navier-Stokes equations are INCORRECTLY stated. The advective term is missing. How can you claim to offer insight to equations which you seem incapable of even stating correctly? For the correct formulation read the wiki page or any book or any paper. This is the last time I will comment on this issue. 203.217.26.35 (talk) 20:01, 15 February 2014 (UTC)

Sorry, I apologise, I myself misread your choice of notation. In any case, the article still is not of general interest. It is not published in a reputable journal and it's sole citation is a self-citation. 203.217.26.35 (talk) 21:24, 15 February 2014 (UTC)

So I had another very brief look at your paper and noticed that (7) is clearly wrong. 203.217.26.35 (talk) 23:39, 15 February 2014 (UTC)

Read carefully an additional proof of (7): 3.3. Proof of Equation (7) from the Point of View of Continuum Mechanics--94.153.74.179 (talk) 08:45, 16 February 2014 (UTC)

I don't need to, what you wrote implies that for the unforced Navier-Stokes equation, the pressure is a harmonic function (see subsection 3.2). You can construct explicit counterexamples to this statement. Set viscosity as zero and the density as 1 to obtain the Euler equations. Now read about stationary solutions to Euler and you can construct a counterexample yourself. If you are unable then ask on http://math.stackexchange.com/ 203.217.26.35 (talk) 10:39, 16 February 2014 (UTC)

Note that the Euler equations (fluid dynamics) have no sense as exact vector equations because gradp is not a true vector! http://books.google.com/books?id=FC0QFlx12pwC&pg=PA15%7CDubrovin, Therefore this counterexample is unsuitable.--94.153.74.179 (talk) 19:30, 16 February 2014 (UTC)

What are you talking about?!?!?!? I think this is a good point to end this conversation, as clearly if you make such comments then there is no point in continuing this discussion. 20:14, 16 February 2014 (UTC) — Preceding unsigned comment added by 203.217.26.35 (talk)

I expected more rigid comments. However look attentively the link and try to comment it.--94.153.74.179 (talk) 21:16, 16 February 2014 (UTC)

This is not the place to teach you that the gradient of a differentiable scalar function is a vector field. You also posted this rubbish on Terry Tao's blog, to which he kindly responded.

Multiple editors have attempted to remove your nonsense paper from the wiki. You retract the edit citing vandalism. The only one vandalising the wiki is you through self promotion. This is not the place. If you believe you have made a significant contribution to this problem then submit your result to a top journal.

Stop wasting your time and other people's time on this pointless persuit.

The other 'published' result has a broken link and so I assume it was retracted. Stop re-adding that as well! I assume it was as 'correct' as all the other so called results you can find on this talk page.

Above claim is only emotions without any proofs. In mathematics the emotions are unsuitable proofs! --5.45.192.102 (talk) 14:25, 25 July 2014 (UTC)

Having a mathematical conversation with you does not lead anywhere (see above).

From a wiki perspective, you have violated two wiki rules: WP:COI, WP:RRR. Your content does not meet accepted notability condition: see .http://en.m.wikipedia.org/wiki/Wikipedia:Notability and http://en.m.wikipedia.org/wiki/Wikipedia:Notability_(science) . Indeed the only one to cite your paper is yourself. You do not get to decide whether your work is notable: that is for the broader community to decide.

It seems you are misusing wikipedia in order to obtain exposure for your paper that you (and only you) believe it deserves. You have posted your paper on Tao's very visible blog and so I can ensure you it has been seen. If any of us believed it had any merit we would be citing your work which we clearly are not.

I will make one last (and possibily unwise) attempt to demonstrate your error. You seem to have misunderstood the chain rule -- you might want to retake 1st year mathematics classes before making big claims about Millennium prizes.

As I said (7) is wrong, you prove this equality with (5*). Now suppose ${\dot {u}}=(y,x,0)$ , then ${\frac {\partial {\dot {u}}_{x}}{\partial x}}={\frac {\partial {\dot {u}}_{y}}{\partial y}}=0$ and ${\frac {\partial {\dot {u}}_{x}}{\partial y}}={\frac {\partial {\dot {u}}_{y}}{\partial x}}=1$ .

Now (5*) implies ${\frac {\partial {\dot {u}}_{x}}{\partial x}}{\frac {\partial {\dot {u}}_{y}}{\partial y}}={\frac {\partial {\dot {u}}_{x}}{\partial y}}{\frac {\partial {\dot {u}}_{y}}{\partial x}}$ or in order words $0=1$ . See the problem?

19:22, 26 July 2014 (UTC) — Preceding unsigned comment added by AnonymousMath (talk • contribs)

I well know about this very interesting problem! This problem is discussed here http://analysis3.com/Helmholtz-decomposition-contradictions-download-w117376.html --5.45.192.94 (talk) 12:59, 27 July 2014 (UTC)

No you obviously do not. This has nothing at all to do with the Helmholtz decomposition. This is is basic vector calculus that you seem to be lacking. You do not understand the chain rule and you seem also not to understand what a gradient is (going by comments on the Euler equation). Quite simply you do not understand very basic concepts in mathematics. You begin by stating something completely wrong (on the level of 0=1) and then using this incorrect calculation you prove other incorrect statements. As I have repeatedly said it is pointless discussing mathematics with you as you have demonstratively complete ineptitude. It is like speaking Chinese to someone that doesn't speak Chinese.

As I have said none of this matters. Your work has been seen by the community. If we decide it has merit we will give you credit. This is how academia works. You are but one of many people that have made erroneous claims regarding the Navier-Stokes Equations (see above), some even have positions at respected universities, and have published in respectable journals.

AnonymousMath (talk) 16:05, 27 July 2014 (UTC)

1. Read attentively http://analysis3.com/Helmholtz-decomposition-contradictions-download-w117376.html 1.Introduction after the formula (5) and you will see your error concerning a gradient. You also can understand why your example gives the unexpected result 1=0.

2. You also write «Your work has been seen by the community». In that case why mathematicians cannot deny this work as rapidly as, for example, Otelbaev’s work?

3. In the absence of arguments you and other Wiki editors can not deny but only block any information about this work. --5.45.192.103 (talk) 12:37, 28 July 2014 (UTC)

It gives 1=0 because it is wrong. Your result implies 1=0, so there are two options, either 1=0 or your calculations are wrong, there is no third option. I have given you arguments why your work is wrong, you just refuse to listen to them. And no, it is not up to us to prove to you that you are wrong. It is up to you to convince the community (and not through Wikipedia) that you are correct. Something you have failed to do. I will point out that you have already been called out for breaking Wikipedia rules (https://wiki.riteme.site/wiki/User_talk:5.45.192.102), have a history of posting your wrong calculations on Wikipedia (https://wiki.riteme.site/wiki/Talk:Helmholtz_decomposition#Helmholtz_decomposition_is_wrong) and have been corrected by Terence Tao (http://terrytao.wordpress.com/2014/02/25/conserved-quantities-for-the-euler-equations/#comment-273035).

Mathematicians critiqued Otelbaev's work because he is a mathematician (http://scholar.google.de/citations?user=kh5yuKwAAAAJ&hl=en&oi=ao), you are not (http://scholar.google.de/scholar?hl=en&q=Alexandr+Kozachok&btnG=&as_sdt=1%2C5&as_sdtp=). Otelbaev accepted his mistakes, you just redirect to other work which is wrong. What is the point with arguing with someone that won't admit they are wrong? This is why mathematicians do not engage with the likes of you (and it is why it is very unwise for me to engage with you).

Your work contradicts the mathematics that keeps the cars you drive on the road, the planes you fly in the air, the water you drink flowing through the pipes, the house you live in from not falling down. Who should we believe, Euler, Riemann, Gauss, Newton, Helmholtz, Leibniz or you?

AnonymousMath (talk) 13:06, 28 July 2014 (UTC)

Above was my final comment regarding this topic. 1 is not 0 and that will not change any time soon. I need to use my time more productively and I hope Mr Kozachok you will to. I apologize for my sometimes heated commentary, the internet can have that effect of people (http://xkcd.com/386/).

AnonymousMath (talk) 08:08, 29 July 2014 (UTC)

All mathematicians should understand that not each three functions of co-ordinates x,y,z allow construct a vector field. However the great mathematicians Euler, Riemann, Gauss, Newton, Helmholtz, Leibniz, etc. did not know this true. This extraordinary discovery is made by very courageous scientists more 30 years ago. Alexandr Kosachok has confirmed this discovery. You can find this information here http://analysis3.com/Helmholtz-decomposition-contradictions-download-w117376.html (1.Introduction and references).

From your example follows 0=1 because ${\dot {u}}=(y,x,0)$ is not a vector. If you are the courageous mathematician you should recognize this unpleasant thing. --5.45.192.115 (talk) 13:26, 29 July 2014 (UTC)

I know I said it was my final comment, but as it seems you have spend years of your life building a parallel mathematical world on top of a very fundamental misunderstanding of mathematics, I will make one last comment. The map $(x,y,z)\mapsto (y,x,0)$ written in Cartesian coordinates, from the vector space $\mathbb {R} ^{3}$ to the vector space $\mathbb {R} ^{3}$ is by definition a vector field (https://en.wikibooks.org/wiki/Calculus/Vectors), just like how the numbers 1, 2, 3, etc. are by definition integers.

You often quote a number of books on differential geometry and continuum mechanics in order to justify your claims. None of those books contradict what I have wrote, you simply have misunderstood the books. None of these books contradict mainstream mathematics (or for that matter the famous mathematicians I listed). In the theory of differential geometry one need to be careful with to how geometric objects transform (https://wiki.riteme.site/wiki/Covariance_and_contravariance_of_vectors). You often bring up this distinction (for example when you talk about gradients), without understanding what this distinction means. Indeed if one sticks to Cartesian coordinates this distinction is not present. To understand this distinction you need to first understand the chain rule, which appears to be your Achilles' heel.

Indeed none of the authors of those books would agree with your claims. These books assume basic knowledge of vector calculus, a subject that you actively contradict. No mathematician agrees with your claims. If you don't believe me, go to your local university and ask.

Everything you have wrote seems to stem from a misunderstanding of the chain rule (https://en.wikibooks.org/wiki/Calculus/Multivariable_calculus#Chain_rule). From this misunderstanding you have build this parallel world. This parallel world is self contradictory, which is why in this parallel world one can lead to statements like 1=0.

AnonymousMath (talk) 17:07, 29 July 2014 (UTC)

You have written this extraordinary important phrase:

… it seems you have spend years of your life building a parallel mathematical world on top of a very fundamental misunderstanding of mathematics

Therefore I hope you will confirm or deny by means of arguments my previous comments:

"All mathematicians should understand that not each three functions of co-ordinates x,y,z allow construct a vector field."

You agree or do not agree?

"However the great mathematicians Euler, Riemann, Gauss, Newton, Helmholtz, Leibniz, etc. did not know this true.This extraordinary discovery is made by very courageous scientists more 30 years ago."

You agree or do not agree?

"Alexandr Kosachok has confirmed this discovery."

You agree or do not agree?

"From your example follows 0=1 because ${\dot {u}}=(y,x,0)$ is not a vector."

You agree or do not agree?

Also, You have written this wrong phrase:

"No mathematician agrees with your claims."

Read attentively (the last 8 lines of Conclusion) http://analysis3.com/Helmholtz-decomposition-contradictions-download-w117376.html

As you can see you are mistaken.

Also, everything you have wrote, require the mathematical arguments--134.249.238.239 (talk) 13:01, 1 August 2014 (UTC)

Please read WP:NOTFORUM Only peer-reviewed papers should be added to the article (and therefore discussed here). --NeilN ^{talk to me} 13:22, 1 August 2014 (UTC)

Dear NeilN|talk to me!

In that case why the Wiki editors block any information about peer-reviewed papers in the "Partial Results":Navier –Stokes First Exact Transformation, Navier –Stokes Second Exact Transformation? It is the true vandalism! --5.45.192.111 (talk) 20:06, 1 August 2014 (UTC)

Where's the commentary on these papers? These should be treated as good primary sources but we need secondary sources to validate and weigh. --NeilN ^{talk to me} 20:14, 1 August 2014 (UTC)

It should also be noted that the publisher (Horizon Research Publishing) is listed on Jeffrey Beall's list of 'Potential, possible, or probable predatory scholarly open-access publishers': http://scholarlyoa.com/publishers/ AnonymousMath (talk) 22:07, 1 August 2014 (UTC)

Dear NeilN|talk to me!

Here (11 Yet another solution proposed?) http://wiki.riteme.site/wiki/Talk:Navier%E2%80%93Stokes_existence_and_smoothness#Yet_another_solution_proposed.3F you wrote:

...These should be treated as good primary sources but we need secondary sources to validate and weigh.

Which of these 11 links is good secondary source?:

1.TOP NEW NEWS Latest News and Hottest http://topnew.info/navier/navier-stokes-first-exact-transformation

2.Navier Stokes Existence And Smoothness http://www.socialscapes.com/search/navier-stokes-existence-and-smoothness-wikipedia-the/

3.Han Geurdes. A simple exact solution to the Navier-Stokes equation JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS J. Part. Diff. Eq., Vol. x , No. x (200x), pp. 1-5| http://www.academia.edu/8480418/A_simple_exact_solution_to_the_Navier-Stokes_equation

4.BOOKSREADR.ORG in the social media http://booksreadr.org/pdf/navier-stokes-millennium-prize-problem-alternative-solution-194170446.html

5.Проблема тысячелетия (millennium prize problem) для уравнений навье – стокса разрешима классическими методами математической физики козачок А. А., Киев, Украина http://ru.convdocs.org/docs/index-2701.html

6.LATEST ECONOMIC NEWS 26.09.14, 11:47 am http://www.mensuniquegift.com/article/Navier-Stokes-First-Exact-Transformation/

7.http://quibromlouiled47.soup.io/since/401643144?mode=own&newer=1

8.http://koart.us/rans/rans-blog.html

9.vimeo.com/18185364/

10.http://www.ebookily.org/pdf/navier-stokes-first-exact-transformation-131787617.html

11.http://www.ebookily.org/pdf/navier-stokes-second-exact-transformation-158069333.html

--5.45.192.110 (talk) 11:54, 18 November 2014 (UTC)

Dear NeilN ^{talk to me} and other editors!

Probably you have already considered the list of secondary sources. Therefore I hope you will begin to discuss the revision of this section:

Attempt at solution[edit]

Classical solutions

In 2013, Mukhtarbay Otelbaev of the Eurasian National University in Astana, Kazakhstan, proposed a solution. As a serious attempt to solve an important open problem, the proof was immediately inspected by others in the field, who found at least one serious flaw.^{[otelbaev 1]} Otelbaev is attempting to fix the proof, but other mathematicians are skeptical.

^ Moskvitch, Katia (5 August 2014). "Fiendish million-dollar proof eludes mathematicians". Nature.

Alternative solutions

Terence Tao in 18 March, 2007announced three possible strategies of an alternative solutions if one wants to solve the full Millennium Prize problem for the 3-dimensional Navier-Stokes equation. Strategy 1 “Solve the Navier-Stokes equation exactly and explicitly (or at least transform this equation exactly and explicitly to a simpler equation)” is used in works:

The author of these works Alexandr Kozachok has offered (in February 2008 – Internet , in 2008, 2010, 2012 – INTERNATIONAL CONFERENCE reports, in November 2013 and February 2014 - INTERNATIONAL journal) two exact transformations to the simpler equations. These transformations are executed by well-known classical methods of mathematical physics. Therefore not only some professionals, but also educational, social and many other sites have published or paid attention to these works .

--93.74.76.101 (talk) 20:15, 8 December 2014 (UTC)

A solution to such an important problem as this needs to be submitted to a top-notch journal, and the result reported. If the argument is correct, even unknown authors can succeed through this path, and the journal will be happy to publish. For example, Yitang Zhangs work on the twin-prime conjecture was submitted, accepted, and now has many cites, and lots of follow-up work (showing that others believe the result). Here the journal is of lower reputation (surely less than such an important result would warrant), and the papers have *no* independent cites (the first is cited only by the second, and the second has no cites, according to google scholar). On such an important problem as this, independent verification by experts in the field is needed. Without that it's not notable. LouScheffer (talk) 20:52, 22 December 2014 (UTC)

LouScheffer!You wrote:

“A solution to such an important problem as this needs to be submitted to a top-notch journal, and the result reported. If the argument is correct, even unknown authors can succeed through this path, and the journal will be happy to publish.”

This work is already published in reviewed international journal. Therefore it cannot be published in other reviewed journal. The rules are that. You should know about it.

“Here the journal is of lower reputation (surely less than such an important result would warrant),….. On such an important problem as this, independent verification by experts in the field is needed. Without that it's not notable."

The journal’s reputation is important only for an estimation of difficult mathematical works which are impossible to understand without the authoritative experts. In our case we have two brief articles (3 and 5 pages) which even the student can understand. Also, the expanded proof (by two independent ways!) of the main result occupies only one page. This work has been seen by the mathematical community in 2008 http://sgrajeev.com/almanack/archives/24#comment-28.. As you can see the mathematicians cannot deny this work as rapidly as, for example, Otelbaev’s work on almost one hundred pages. Thus, your last revision must be removed. --93.74.76.101 (talk) 20:46, 24 December 2014 (UTC)

Anonymous IP is a well-known mathematics crank on Wikipedia. See, for instance, here, where he claims that the chain rule is wrong and that the Helmholtz decomposition is wrong. Discussion is pointless. Just revert his edits. Sławomir Biały (talk) 01:57, 30 December 2014 (UTC)

Indeed it seems for a number of years he has been applying his miscomprehension of the chain rule in order to come up with a number of absurd results. He interprets any feedback as positive confirmation of his work, including rejection letters from referees, discussions where others are trying to correct him, and silence, after others get fed up discussing basic concepts of mathematics. So discussion is certainly pointless. Hopefully, he will eventually grow tired of vandalising the wikis he edits. However, since this has been going on for years there doesn't seem much chance of that happening. AnonymousMath (talk) 15:12, 30 December 2014 (UTC)

WP:NOTHERE

The following discussion has been closed. Please do not modify it.

Sławomir Biały, You are the authoritative Wiki editor. Therefore, many readers trust you. However, you deceive them. You have written (01:57, 30 December 2014 )

“…he claims that the chain rule is wrong”.

But (18:26, 25 March 2012) here: https://wiki.riteme.site/wiki/Wikipedia_talk:WikiProject_Mathematics/Archive/2012/Mar#Helmholtz_decomposition_is_wrong you have written:

“Alexandr above claims to have found a counterexample to the chain rule”.

Besides, in the article "Navier –Stokes First Exact Transformation" http://www.hrpub.org/download/20131107/UJAM1-12600416.pdf we can read

“Note that formulas (3*) also well known as chain rule”.

As we can see, your claim is a full disinformation.

AnonymousMath, your comment is only emotional claim without any arguments. In mathematics, the formulas are needed. The expanded proof (by two independent ways!) of a main result in the article "Navier –Stokes First Exact Transformation" http://www.hrpub.org/download/20131107/UJAM1-12600416.pdf occupies only one page! Show, please, which formula is wrong?

Sławomir Biały and AnonymousMath! I wish you a very Happy New Year and ask to begin the fruitful scientific discussion. 93.74.76.101 (talk) 16:24, 1 January 2015 (UTC)

AndyBloch, you wrote:

“Self-promotion of erroneous papers”

The expanded proof of the main result in http://www.hrpub.org/download/20131107/UJAM1-12600416.pdf occupies only one page! Show, please, which formula is erroneous. As you can see above “This is not a forum for general discussion of the article's subject.” Therefore let’s discuss this problem here http://wiki.riteme.site/wiki/Wikipedia_talk:WikiProject_Mathematics#Navier_.E2.80.93_Stokes_Millennium_Prize_Problem._Alternative_Solution 93.74.76.101 (talk) 14:58, 21 January 2015 (UTC)

Nope. We are not a forum. It is not our mandate to find your errors for you. One way to get your errors pointed out is to offer a bounty for anyone finding an error. I think $500 should do the trick, but you should actually be prepared to pay it out pretty quickly. Sławomir Biały (talk) 14:29, 24 January 2015 (UTC)

[1] Moskvitch, Katia (5 August 2014). "Fiendish million-dollar proof eludes mathematicians". Nature.

[otelbaev 1]