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Kazakh Professor Claims Solution of Another Millennium Prize Problem 162

Posted by Soulskill
from the awaiting-peer-review dept.
An anonymous reader writes "Kazakh news site BNews.kz reports that Mukhtarbay Otelbaev, Director of the Eurasian Mathematical Institute of the Eurasian National University, is claiming to have found the solution to another Millennium Prize Problems. His paper, which is called 'Existence of a strong solution of the Navier-Stokes equations' and is freely available online (PDF in Russian), may present a solution to the fundamental partial differentials equations that describe the flow of incompressible fluids for which, until now, only a subset of specific solutions have been found. So far, only one of the seven Millennium problems was solved — the Poincaré conjecture, by Grigori Perelman in 2003. If Otelbaev's solution is confirmed, not only it might be the first time that the $1 million offered by the Clay Millennium Prize will find a home (Perelman refused the prize in 2010), but also engineering libraries will soon have to update their Fluid Mechanic books."
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Kazakh Professor Claims Solution of Another Millennium Prize Problem

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  • by Anonymous Coward

    Oh no. Textbook publishers HATE having to do that....

  • by Frans Faase (648933) on Saturday January 11, 2014 @02:23PM (#45927097) Homepage
    If it is such an important article, why did he not find someone to translate it to English? He did get some related papers published in English. It seems that those are about approximations. Interesting non the less.
    • by qaz123 (2841887)
      Somebody will translate it
    • I think it's common for such papers that aren't written directly in English to only be translated after their original version has been released

      • by Anonymous Coward

        Indeed it is (very) common. It will be translated, in due course, for a broader audience. For a paper like this it's extremely important that a translation is correct, and that takes time. The ones demanding an English version up front need to, frankly, grow up a bit.

    • by Anonymous Coward
      Math papers look prettier when you combine so many alphabets, it feels more like art (incomprehensible art). You get cyrillic (including cursive [wikipedia.org]), greek leters in formulae, and some latin here and there. That's original, I like it.
    • by HiThere (15173)

      Yes. It should be in English, because that's the language I speak.

    • If he's really solved the problem, he's probably in a hurry to get it written up as he may believe that others are close, using similar methods. In that case, he'd write it up in his native Russian and make it public. That way, he's got priority, and the translation can come anytime. But there will certainly be a translation, because many English speaking mathematicians will want to give his work close scrutiny.
  • Great, like the college text books need another reason to come out with a re-write for next year.
    • At least they'd have a good reason this time.
    • by Anonymous Coward

      Hell with the college text books. It's all the CFD (computational fluid dynamics) code that is going to have to be rewritten. Currently, (as I understand it), all this code approximates or partially solves Navier-Stokes for different special cases. Good work if you are the right kind of engineering analyst-programmer.

      • by wagnerrp (1305589)
        All this code approximates, or partially solves, Navier-Stokes for different special cases, because we don't have the computational power to do otherwise.
        • Re:Conspiracy (Score:4, Informative)

          by MickLinux (579158) on Saturday January 11, 2014 @08:06PM (#45928983) Journal

          Okay, define three points, and a fourth point not coplanar with the first three. Now, sum up the area of the triangles defined by the fourth point, and subtract the area of the triangle of the first three. You thus define a field that is zero on the triangle of the first three, but nonzero everywhere else. Now, if you substitute a function for the perpendicular position of point four, you can get a field that is zero on a predefined curved plane, bounded by the three-point triangle.

          Now, divide any arbitrary surface into such triangles, and multiply the fields together, and you will have a field that is zero on the surface of your object, nonzero everywhere else.

          Do this with Parker-sochacki equations, and the solution is computationally simple.

          Now, based on this field define a coordinate system whose air velocity is a function of the field value, and zero where the field is zero.

          Now, again using Parker-Sochacki, plug that into the Navier Stokes equations, under the effect of a body force that is a miniscule fraction of the difference in velocity from your desired free-stream velocity.

          The result will be a mclauren (taylor) series that gives the velocity of the air at any point and time. Since the existance and uniqueness of the Parker Sochacki is already proven, then the existance/uniqueness of the Navier-Stokes solution is also provable.

      • Re:Conspiracy (Score:4, Informative)

        by semi-extrinsic (1997002) <asmunder@@@stud...ntnu...no> on Saturday January 11, 2014 @06:22PM (#45928479)
        You're very wrong on all points I'm afraid. This will have zero impact on any CFD codes. And where did you get the (slightly ridiculous) idea that CFD programs only solve for special cases? It's true that most restrict themselves in some way, e.g. "subsonic and non-turbulent", but otherwise they are completely general. Source: my PhD work consists of writing a CFD code for Navier-Stokes. (The summary talking about rewriting textbooks is also way off on their understanding. This will likely be incomprehensible without a PhD in the right area of mathematics.)
        • This is Slashdot on a Saturday night. There are going to be at least 15 people who are convinced they know more and better than you buddy...
  • by Frans Faase (648933) on Saturday January 11, 2014 @02:45PM (#45927209) Homepage
    In his bio [otelbaev.com] it is claimed that he found explicit formulas for n-particle motion in the space (in the framework of Einstein’s relativity theory). If that would be true, I guess it would have be known in the rest of the world as well, if he had.
    • While it's probably hard mathematics I do not think that finding a bunch of explicit solutions to such problems is likely to be all that novel.

      While It might sound as if though it's a claim to have found an explicit formula for n-particle motion in every case, it's fairly clear that they're talking about particular cases. It also seems unlikely that he makes trivial errors given that he got a PhD from MSU.
    • by jd (1658) <.imipak. .at. .yahoo.com.> on Saturday January 11, 2014 @04:37PM (#45927875) Homepage Journal

      Well, yes and no. There is no general solution to the n-body problem, where n is greater than 2. The nature of the system makes that inevitable. The system isn't differentiable and you can't actually perform infinitesimal steps.

      What you can do is define bounds for certain special cases, where the solutions must exist within those bounds. The error on the bounds increases quite quickly, which is why space probes are forever making course corrections. Bounds do not exist in all cases, as three bodies is sufficient for the system to be chaotic (deterministic but not predictable), which means in those cases, you rely heavily on probability (meteorologists perform hundreds of thousands of simulations and see what general patterns have the highest probability of cropping up) and on very short timeframes (in snooker, you can make a reasonable guess as to what will happen one or two reflections ahead).

      These are inescapable properties of multibody dynamics, because you can do bugger all with infinite multiway recursion. There is no way to simplify it... ...as it is.

      What you CAN do is flatten the universe into a 2D holographic model. If there is no time, there is no place for recursion. That might yield something. Alternatively, with time dilation, you can make infinitesimal time arbitrarily large. Neither of these will yield an absolute answer, but could be expected to yield an answer that looked as though it was.

      • Holographic: I do not think it means what you think it means.
        • by jd (1658)

          I understand the Holographic Universe theory perfectly well. And nothing can excuse Princess Bride Memeology. Now gerroff my lawn!

      • Wow, my Saturday math lesson. Thanks.
        • by jd (1658)

          Maths and philosophy are directly interchangeable. This is why camels are so confused.

      • by Anonymous Coward

        There is no general solution to the n-body problem, where n is greater than 2. The nature of the system makes that inevitable. The system isn't differentiable and you can't actually perform infinitesimal steps.

        That's bull. The system is perfectly differentiable (in fact, that's how you write the equations of motion) and you cannot perform infinitesimal steps for any system. Numerical solution use finite discretization, which is a decent approximation for well-behaved solutions and fails for chaotic ones (such as n-body general problems). The actual problem is that there's no general closed-form solution, and approximations break down due to chaotic behavior in the majority of cases. However, there exist particula

        • by jd (1658)

          You are confusing setting up a system of differential equations (which you can do) with the system being differentiable (which is quite another matter).

          Your post largely restates what I stated, so as far as I am concerned, you are more concerned with being pompous than with comprehending what it is you are being pompous about. Wake me up when you grow enough of a pair to read as well as write.

          • by MickLinux (579158)

            Arxiv.org/pdf/1007.1677

            The solution is published there, and easy to understand.

            Considering that the Taylor series is an exact solution, and existance /uniqueness of the solution has been proven, one can.definitively say that the solution is numerically differentiable. That is not CFD/FEM. That is an exact solution.

    • by MickLinux (579158)

      I believe his claim. My father published the solution to the n-body problem: it involves applying the Parker-Sochacki solution to the Picard Iteration to celestial mechanics.

      Google it. His tutorial is easy to understand and use for other applications.

      http://csma31.csm.jmu.edu/physics/rudmin/parkersochacki.htm [jmu.edu]

      Arxiv.org/pdf/1007.1677

      Why do I believe his claim? Because although Parker and Sochacki independently came up with their solutions, my father believes that others have as well: an italian guy seems to h

  • Eurasian National University?
    I thought 1984 was fiction...

  • Not a crazy (Score:5, Insightful)

    by Anonymous Coward on Saturday January 11, 2014 @03:11PM (#45927325)

    Otelbaev has published in some very respected journals, and trained with the very top people. His work is worth serious scrutiny. Of course, it is easy, even for the most brilliant scholars, to make a mistake which makes it look as if a big problem has fallen. Skepticism, but no mockery, please.

  • ...mathematics, but real fluids are compressible, viscous and varying properties. Let's see how far his approach extends and how closed the answers are. Fluid mechanics text book publishers will probably give him a few paragraph boxes or pages for history and theoretical stuff. Then back to the classic stuff.

    You can solve minor physics problems starting in their relavistic form, but most engineers still use Newtonian physics.
    • by Anonymous Coward

      ...mathematics, but real fluids are compressible, viscous and varying properties.

      Water, and many similar fluids, are effectively incompressible (except when considering the largest scales). As a specialist in fluid dynamics, I could care less what people do with compressible fluids. The field is more or less split 50/50.

  • by Anonymous Coward on Saturday January 11, 2014 @04:11PM (#45927717)

    I take exception to the use of the word "Claim" here. I never see this used for American or Western professionals?

    In fact here on Slashdot we have a story about "Cheshire Cat" observations by a group and "Claim" wasn't used there.

    You (Slashdot) are being highlighted for your stereotypes and western aligned views again.

    • Re: (Score:3, Insightful)

      by wagnerrp (1305589)
      It has nothing to do with nationality. It has to do with finding a solution to a prominent problem, widely used in industry, that has gone unsolved for well over a hundred years. If you do something evolutionary, or something no one else has done before, then there's no history on which to base doubt. If you do something where so many others have already tried and failed, then inductive logic dictates skepticism until you have independent verification otherwise.
    • by glwtta (532858)
      Hard to say, I guess we'll find out what wording Slashdot chooses to use when a Westerner solves a Millennium Prize Problem?
  • Director of the Eurasian Mathematical Institute of the Eurasian National University

    Kazakhstan and all the 'stans' are in Asia. Why do they have to pretend to be associated w/ Europe by using the term 'Eurasian'? The only 2 Eurasian countries that exist are the Russian Federation and Turkey. Russia since west of the Urals is Europe and east of it is Asia. Turkey since Anatolia is in Asia while the East Thrace part of the country is in Europe.

    But none of the other countries are 'Eurasian'. Georgia and Armenia might be considered European, since they culturally have little in common w

    • Re: (Score:2, Informative)

      by Anonymous Coward

      Look mommy, I did a Google [wikipedia.org].

      Was your post plain ignorance or a bit of bigotry? I can't quite tell.

      • by unixisc (2429386)

        Why would it be bigotry? I was just pointing out that not every Europe wannabe country is a part of Europe. If Mongolia or Japan or India wanted to define itself as a part of Europe, would it? This is like the Lincoln question about a dog's legs.

        I checked your link, Hon, and the case for Kazakhstan being in Europe @ all are hardly there. In most continental maps, Kazakhstan used to be shown solely in Asia, while the Ural mountains & river were the parts demarcating European & Asiatic Russia.

    • by oldhack (1037484)
      Shut the fuck up. Europe isn't even a real continent anyways.
    • by Cochonou (576531)
      There is a growing trend to count Europe and Asia as a single continent (Eurasia), because physically they are a single entity.
      • by unixisc (2429386)
        In that case, this is new. Previously, countries like Britain, France, Germany, Sweden, et al were European countries, while countries like Japan, Korea, Taiwan, India, Israel, et al were Asian countries. So now, all of these are Eurasian countries?
        • by Cochonou (576531)
          Yes, this is something rather new, and of course this is not used by everybody - by far. I believe this trend has more traction in Asia than in Europe, that is why you'll see more Asian countries being called "Eurasian" than European countries.
  • by TroyHaskin (1575715) on Saturday January 11, 2014 @10:21PM (#45929661)
    The post states that the paper "is claiming to have found the solution to another Millennium Prize Problems" while the article's title is “Existence of a strong solution of the Navier-Stokes equations". By my interpretation, the paper is claiming to show the existence of strong solutions (that is, solutions satisfying the Navier-Stokes equations in non-Weak Form subjected to some set of boundary data) not a general (or any) solution, in particular. While the proof of existence is the Millennium Prize if the proof includes smoothness (continuity after some degree of differentiation), the fact of whether or not these solutions exist is irrelevant to most (if any) Fluid Mechanics texts and engineers/modelers.

    The post also states that the Navier-Stokes is "fundamental [set of] partial differentials equations that describe the flow of incompressible fluids"; this is true if all the physical parameters (density, viscosity, and pressure) are taken as constants such that an equation-of-state and energy equation are not needed. However, if they are not assumed constant, the Navier-Stokes equations also perfectly describe the flow of compressible fluids if equipped with an energy equation, an equation-of-state, and other constitutive relations as needed. The only rub comes in when dealing with a fluid that is either not a contiguous field (such as fluids that break-up when immersed in another or, in some cases, a fluid undergoing phase change) or a fluid that does not obey the Stokes Hypothesis (an extension of the idea of a Newtonian fluid to multiple dimensions) which is used as a constitutive relation for the stress tensor in the Navier-Stokes equations.

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