[startingWithCFD]

http://www.spiegel.de/wissenschaft/m...-a-943228.html

The article is in German. It says that a mathematician from Kazakhstan (Muchtarbai Otelbajew) has published a 100-page paper on the existence of strong solutions for the NS equations. The paper is written only in Russian for the moment.

Exaggerated claims from the journal perhaps (or the mathematician)?
Or are we all out of work? ;-)

[wyldckat]

I'm not a specialist in CFD, far from it.
But from what I've learned so far (only bits and pieces ), it's always been known that strong solutions for the NS equations do exist, but they are computationally too heavy to solve them directly.

[yzeyue]

I also have a question whether the DNS is precise for CFD, and if DNS is precise with the only problem of must be in super computer-----a seemingly easy solved problem, why people still research LES...?

[flotus1]

Originally Posted by startingWithCFD

Or are we all out of work? ;-)

Even if this claim turns out to be true, dont worry about unemployed CFD engineers
Basically it only means that what we have been doing for the last decades (numerically solving equations derived from the NS equations) was not entirely wrong.

why people still research LES

Because the supercomputers fast enough to perform DNS simulations for flows at high Reynolds numbers (e.g. flow around cars or planes) wont be available before the end of this century. If ever...

[truffaldino]

Originally Posted by wyldckat

I'm not a specialist in CFD, far from it.
But from what I've learned so far (only bits and pieces ), it's always been known that strong solutions for the NS equations do exist, but they are computationally too heavy to solve them directly.

Mukhtarbay Otelbaev has claimed that he solved one of 7 millenium problems namely the problem about existence of smooth solution of NS equation in R^3 (the problem is stated on the Clay's institute page http://www.claymath.org/sites/defaul...vierstokes.pdf).

Here there is an article about the author of solution in English: http://bnews.kz/en/news/post/180213/.

The only millenium problem solved so-far is the Poincare Problem (solved by G. Perelman who rejected 1000000 $ prise from the Clay Institute).

I do not know if the claim about NS problem is serious. Will wait until experts will say their word about this work.

[FMDenaro]

http://www.claymath.org/millennium-p...lennium-prizes

[truffaldino]

I found a thread on the same topic in the same forum posted several days ago:

http://www.cfd-online.com/Forums/mai...otelbayev.html

It is interesting that the Clay Institute page never mentions word "Turbulence", they talk about existence of smooth solution only. It is interesting are there any direct and useful link (something like Kolmogorov theory) between problem of existence and description of turbulence.

[FMDenaro]

Originally Posted by truffaldino

I found a thread on the same topic in the same forum posted several days ago:

http://www.cfd-online.com/Forums/mai...otelbayev.html

It is interesting that the Clay Institute page never mentions word "Turbulence", they talk about existence of smooth solution only. It is interesting are there any direct and useful link (something like Kolmogorov theory) between problem of existence and description of turbulence.

well, maybe the direct link is the existence of the strong solution that would ensure the fact that turbulence is governed by a strong solution of NS equations?

[truffaldino]

So, does that means that all possible singularities (at smooth initial data) die in the framework of incompressible NS at Kolmogorov scale, without need to modify equations to compressible, or nonlinear stress etc.

BTW, is the problem for the compressible NS more complicated?

P.S. I found partial English translation of Otelbaev's article here https://github.com/myw/navier_stokes_translate

[FMDenaro]

the compressible form of the NS enters into thermodinamic issues and I think that finding an existence and regularity proof of the solution is a very different matter....