What is the validity of the supposed solution to the Millenium Problem?

[truffaldino]

Hello,

Recently it has been announced on the web that a progessor from Kazakstan has solved the Clay institute millenium problem showing existence of strong solution of Navier-Stokes (see eg https://github.com/myw/navier_stokes_translate).

I do not know if it is true or not, but reading introduction to his article I got an elementary question.

He says that the proof of existence for a liquid initially at rest u(x, t=0)=0 subject of action of sufficiently smooth force is equivalent to existence for starting with non-zero sufficiently smooth initial data (as required by the Clay Institute).

From the intuitive (physical) point of view that looks obvious (the system with smooth solutions can be driven to any desired state by properly chosen force).

But what is the formal proof (must be something elementary).

Thanks

 

[truffaldino]

Seems that was a silly question?

The answer is indeed elementary: Take any divergence free function of (x, t) that ends as initial data at some t_0 and is zero at t=0. Then substitute it into the NS equation and get f(x,t) and p(x,t).

The problem is choosing the divergence free function, but this looks like the trivial one.

Edit: It is indeed the trivial one, just take initial data and multiply by g(t) with g(0)=0 and g(t_0)=1

 

[gravenewworld]

Here is another article on this:

http://www.newscientist.com/article...012-GLOBAL-facebookgoogletwitter#.UuL-Vnko6c9

 

[Dadface]

Since when has it been difficult to evaluate a work because it has been written in a certain language? Russian speaking mathematicians can evaluate the work and when translations become available other mathematicians can take a look.

(This is referring to the New Scientist article above)

 

[dextercioby]

Back in the vicious Cold-War days, Russian mathematicians often got their papers and books translated into the English-version of the their journals. Now in 2014 it's quite appalling to have someone outside US/UK write a page into other language than English...

 

[AlephZero]

Since when has it been difficult to evaluate a work because it has been written in a certain language?

The best way to answer that question is, try it for yourself (even with a paper written in your native language, on a topic that you know something about).

Research papers don't spell out every step of an argument in the same way that textbooks do, and the errors are unlikely to be "obvious" mistakes.

 

[Dadface]

The best way to answer that question is, try it for yourself (even with a paper written in your native language, on a topic that you know something about).

Research papers don't spell out every step of an argument in the same way that textbooks do, and the errors are unlikely to be "obvious" mistakes.

I'm not suggesting that evaluating the work should be easy. I was responding to the New Scientist article and suggesting that language should not be a barrier.

 

[Tobias Funke]

Aren't some mathematicians also complaining that they can't follow the purported ABC proof because the author isn't spoon-feeding them, and they have to actually spend time learning new math?

It's not written in Klingon for crying out loud, millions of people speak Russian.

 

[AlephZero]

I was responding to the New Scientist article and suggesting that language should not be a barrier.

"Traduttore, traditore."

 

[Dadface]

"Traduttore, traditore."

I would be surprised if there weren't translational difficulties but they are not insurmountable and any good translator should be able to come up with suitable alternatives which convey the same meaning.

 

[AlephZero]

There is also a lot of money at stake here. Let's take a hypothetical situation which is not entirely implausible:

Alice writes a paper in Russian. There are several mistakes in the detailed logic of the paper.

Bob knows a small amount of Russian, but a lot of math. Bob reads the paper and decides it is correct. He didn't notice the mistakes, because he just read the equations, and skipped the words in between because his attempts to translate then didn't make any sense. So he didn't know that Alice got to the right "answer" for the wrong reasons.

Now: who should receive the $1m prize? Bob would say "Alice". Somebody who knew more Russian might say "Bob".

 

[Dadface]

Even if there weren't a lot of money involved a paper of such wide ranging interest and potential importance is lkely to be far more thoroughly scrutinised than is normal. I can imagine it being checked by all sorts of interested parties, initially by Russian speakers and later by others when translations into different languages become available.
True that mistakes can be made and perhaps even slip through the net, but the strongest possibility is that any mistakes will, eventually be spotted.

 

[gravenewworld]

Since when has it been difficult to evaluate a work because it has been written in a certain language? Russian speaking mathematicians can evaluate the work and when translations become available other mathematicians can take a look.

(This is referring to the New Scientist article above)

Other Russian speaking mathematicians have:

Otelbayev says that three colleagues in Kazakhstan and another in Russia agree that the proof is correct.