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Navier&Stokes to follow Poincare?

  1. Oct 7, 2006 #1
    Navier&Stokes to follow Poincare??

    It seems that yet another important problem in mathematics, and more importantly in physics, may have been solved. This time it's the Navier-Stokes Equation. This, too, is on the Clay Mathematical Institute's list of Millenium Problems. I've seen a couple of blog entries in the past week on this, so here are all the links...

    [URL [Broken]
    Immortal Smooth Solution of the Three Space Dimensional Navier-Stokes System[/url][Arxiv]

    http://www.claymath.org/millennium/Navier-Stokes_Equations/ [Broken]


    Obviously, I can't make head or tail of all this, so the pros here can decide whether it's worthy enough of the award. :tongue2:

    To the mods: I've posted this in General Math section based on the author's choice in the Arxiv.
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Oct 7, 2006 #2


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    Dearly Missed

    If this holds true, then it is a great advance.

    I'll try to get a head of this, but I'm not sure if I manage to attach its tail properly.

    Thanks, neutrino!
  4. Oct 7, 2006 #3


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    Yeah, I called my local newspaper yesterday to see if they wanted to run a note mentioning this.
  5. Oct 8, 2006 #4
    Did they understand you?
  6. Oct 8, 2006 #5
    when i looked at that columbia blog page one of the last comments said pennny's paper had been 'withdrawn'. the person didnt say what was wrong with the proof but it looks like 'false alarm'.... for now.
  7. Oct 8, 2006 #6
    Thanks for that, fourier jr. Looking at the arxiv link, one can see that it has gone through a few revisions in the past week.
  8. Oct 8, 2006 #7
  9. Oct 8, 2006 #8


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    That looks like quasi-math by someone who doesn't know TeX.
  10. Oct 8, 2006 #9
    You can't judge a book by its cover...:mad: :frown: :mad: if you were "ugly" would yo like to be judged by your physical aspect?.

    Of course i have read by didn't understand most of it, at least i think the author is trying to say us that the "Trace" of the operator [tex] Tr(u)=e^{iu\hat H} [/tex] exists and is related to the derivative of a certain numer-theory function, and that the potential satisfies (as seen on the wikipedia)

    [tex] Tr(u)u^{1/2}\sim \int_{-\infty}^{\infty}dxExp(iuV(x)+0.25i\pi) [/tex]
  11. Oct 8, 2006 #10
    "Authors: Penny Smith
    Comments: Withdrawn
    Subj-class: Differential Geometry; Analysis of PDEs
    MSC-class: 35Qxx

    This paper is being withdrawn by the author due a serious flaw. "

    Looks like false alarm.
  12. Oct 8, 2006 #11

    matt grime

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    It is going to take some convincing for me to believe that you are not Jose. Every post you make just emphasises the point that you are indeed he, and attempting to foist off this nonsense as if it weren't is intellectually dishonest. If you weren't he then why get bothered abuot the comments on its presentation?

    Of course there could be two people who post on identical topics here, in identical fashoin, I suppose. And you might not be at all related to the Jose of that post on the arxiv. But twice now you've put a link to it, just raising suspicions once more.
    Last edited: Oct 8, 2006
  13. Oct 8, 2006 #12
    "In September 2006, Penny Smith of Lehigh University posted a paper on arXiv claiming to "prove the existence of a smooth solution for all time--under physicially reasonable hypothesis on the initial data--for the Navier-Stokes System in three dimensions."[1] On October 8, 2006, this paper was withdrawn by the author due a serious flaw."

    From Wiki


    Interesting how this unfolds, Andrew Wiles also found a major flaw in his proof of FLT, but quickly corrected it. I mean if this error is too serious that undermines the whole proof.
  14. Oct 9, 2006 #13
    Penny Smith's paper may have been withdrawn but this recent solution to the Navier-Stokes equations by David Purvance is still standing:

    http://arxiv.org/abs/math.AP/0610086" [Broken]

    The Arbitrarily-Close and Convergent Fer Product Solution to the Three Spatial Dimension Navier-Stokes Equations.
    Last edited by a moderator: May 2, 2017
  15. Oct 21, 2006 #14

    Gib Z

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    If they really have found solutions then this shud be headline news lol, because these equations have been found to describe the motions in the universe, which is obviously surprising as these equations were orignally intended to describe fluid motion, correct me if im wrong. And also, all of us here, talking as if we know anything about the Riemann hypothesis, like were all mathmaticians. seriously, i swear if ANYONE knows crap about it, its matt grime, and even he probably has troubles understanding the proof. I swear, we all think were smarter than we really are.
  16. Oct 21, 2006 #15
    Like everyone knows what's really happening inside the White House, or Iraq, or N.Korea. This is just math gossip, and everyone who is anyone can gossip. :tongue2:
    Last edited: Oct 21, 2006
  17. Oct 21, 2006 #16

    matt grime

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    I know very little about the Riemann Hypothesis (and since there isn't a proof of it, Gib I certainly can't understand that).
  18. Nov 2, 2006 #17


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    Who was this Penny Smith?

    And if you "solve" NS, are arxiv and a blog good places to get comments from?

  19. Nov 2, 2006 #18
  20. Nov 2, 2006 #19


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    Penny Smith is from what I've heard a ~40 year old doctoral student.
  21. Nov 2, 2006 #20
    Wow! She must be good then; especially with a Ph.D at age 12.

    # Penelope Smith

    * Associate Professor (on leave)
    * Ph.D., Polytechnic Institute of Brooklyn, 1978.
    * Differential geometry and geometric measure theory

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