No, this is not yet peer reviewed.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:
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:
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.
His paper may contain errors, but he's not a crank.
In  I learned that it is known that certain differential equations associated with embedding manifolds in R^n possess no smooth solutions. And in  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.
(See Willie Wong's answer)
There is a small summary at the end in English, although it only seems to cover the problem:
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
"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."
Is this relevant to the topic?
ps. Never mind, I guess this answers the question.
I think it would be funny if someone really went just that far, though: give an existence proof for a solution that is not constructive.
Because of that, I would find it more 'enjoyable' to see a proof that a polynomial time algorithm for TSP exists, than to see a proof by example, or to see a proof that go is a win for white or chess for black than to see a program that plays the game perfectly (and of course, within the space of constructive proofs, there are gradations. Exhaustive search would be extremely dull; a theory that generalizes to other problem spaces would be more interesting. Moving to another problem the various O(<n^3) matrix multiplication algorithms are 'funny' because, AFAIK, none of them has practical use.
From a computer science perspective, this would be favorable, as a solution for NP-hard would render a lot of crypto useless overnight. =P
If crypto relies on some algorithms that are O(n^100000000000) where n is key length, I'm not very worried.
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
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.
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...
TL;DR People who work on geometry knew Perelman pretty well.
>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.
while i don't know anything about this guy, beside one in 1976, the Google citation index seems to show only ones in current century.
Quick search from other link http://www.ecosecretariat.org/ftproot/High_Level_Meetings/Su... :
"He contributed in the development of mathematics, for which he was awarded to the prize of the Department of physics-mathematical sciences of AS [Academy of Sciences] of USSR in 1990. He published 200 scientific papers and monographs."
I'm sure that this guy did have at least some citations between 1976 and 2000 :)
It is in Russian
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.
Faraday's original approach was the "flow" of the field
( that was later mathematized by Maxwell).
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 ?