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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."
'more that', instead of 'more that'
So much irony it is delicious...
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.
great. another reason for "oh, you need to buy new textbooks for the class this semester".
Sleep your way to a whiter smile...date a dentist!
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.
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.
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
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.