Kazakh Professor Claims Solution of Another Millennium Prize Problem

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."

Re: Hopefully correct but will wait for verificati

[techprophet]

It's P=NP, you insensitive clod!

Re:It kind of makes me sad...

[Anonymous Coward]

"To each according to his contribution" is a core tenet of Socialism, not "aping Capitalism." Paying people more for greater labors is not the defining aspect of Capitalism --- rather, it's whether people are allowed to use their money to control the labor of others and accumulate an ever-growing cut for themselves without working (a Capitalist class who gets richer as a reward for being rich, while controlling the work/lives of the majority). None of the former Soviet-bloc countries considered themselves to be at the "full-blown Communism" stage, where abundant goods were distributed to all regardless of work input. "Socialism," as defined in the Marxist framework with an end goal of Communism, is in no way contradictory with paying hard workers more (but for their own use/enjoyment, not for authority over other people Capitalism-style).

Re:Why not in English?

[Anonymous Coward]

Einstein's early publications would have had Russian translations or might even have been written in Russian first. It was the lingua franca of science at that time.

I think you're confusing "Russian" with "German," which was a major scientific language of the time (and, indeed, used in Einstein's early papers). Russian became a major scientific language during the mid 20th century, when scientific research was carried out in parallel on both sides of the "iron curtain" (frequently resulting in near-simultaneous discoveries and advancements, independently worked out by research groups on both sides).

Re:His bio: Solution for n-particle problem

[jd]

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.

Re:Conspiracy

[semi-extrinsic]

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.)

Re:Eurasian?

[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.

Re:Conspiracy

[MickLinux]

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.

Two misleading statements

[TroyHaskin]

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.