Hello!
I am sharing draft of Navier-Stokes Existence and Smoothness problem solution:
navier-stokes.ateravis.com
Any feedback is much appreciated!
BB
>>7651800
Oh look its this guy again
>>7651800
Is this a legit attempt or did you seriously waste time writing 80 pages of bullshit?
>>7651800
hi my name is Terence tao. This solution is absolutely incorrect. please stop trying to further it
>>7651857
absalutly don't know wtf any of that means but now I'm curious why is it wrong in a dumbed down verion
I do not think that someone here could prove you are right.
Unfortunately.
Is it a recent attempt?
>>7651838
Thanks for your sincere feedback. I would kindly ask to justify your opinion using facts. I hope that I documented enough of facts both in intuitive and formal form, for ones willing to read it.
Unfortunately, people wasted and are still waisting lots of time working this issue, completely detached from reality. Detachment from reality is embodied in divergence free condition in this particular case. This attempt will hopefully sooner rather than later spare others waisting their time.
Dr. Tao, I believe that you are not correct!
If you believe that something in shared document is not correct, please provide justification instead of speculating and labelling, which is definitely neither scientific nor professional.
It is very unfortunate that people are wasting time analyzing mathematical models which include interpretation of abstraction in form of 'divergence free condition' as solenoidal fields only, as use of such cannot result in 'physically reasonable' mathematical outcome. People close to abstracting 'physical reality of nature' and familiar with 'conservative' and 'non-conservative' fields, know that any 'physically reasonable' model must be of conservative nature, which is not the case for vector fields which velocity has curl<>0. Conservative physical systems can be modelled in form of gradient of scalar potential, which divergence could be zero for harmonic functions:
https://www.youtube.com/watch?v=bamvEE9_oQ8
As per Helmholtz theorem (with some reasonable conditions), vector field could be broken into components of gradient of scalar function and curl of another vector field. If solenoidal component is zero, what is left is gradient of scalar function which is conservative and could be divergence free for harmonic functions, as divergence of gradient of scalar function is Laplace equation for which solution is harmonic. Therefore, gradient of harmonic solutions (without solenoidal component) would be divergence free but not incompressible - it would be divergence free and compressible, which is fine.
Solenoidal vector fields are simply not conservative, and as long as those simple facts about Reality of Nature are ignored, blowups in mathematics will be happening, which does not matches experience and experiments in reality.
Therefore, I appreciate advice to stop to furthering this, however, truth cannot be told what to be and what to do, and I will support it all the way.
Any additional comments would be much appreciated.
I don't have time (or desire) to read this in detail but I can't help but notice that this is not math.
At best a very handwavy interpretation of it.
Besides, you say Millenium Problem too much, your algebra is shaky and your conclusions are wrong
So what? There are like 7 of these on arXiv every day. Until your solution is in a journal, nobody will read it.
I do think NS will be the next millennium prize problem solved though.
>>7653720
Please clarify what in language of math means 'shaky' and how can anything be concluded as wrong without reading?
Incompressible fluid is like pile of 'infinitely small' and tightly packed ball bearings. Question asked regarding NS problem, translated to intuitive language is 'given this NS equation for fluids, if you have unlimited universe full of tightly packed ball bearings, can you show how fluid flows, or prove that it cannot be done'... There is no way that universe stuck with jammed ball bearings would do anything else than keep moving as when t=0. Good luck with getting funds to describe imaginary world of why math breaks...
Is it 'physically reasonable' to expect that incompressible fluid would not compress if thrown into a black hole? As per its definition black hole cannot compress a bit of it. It is much closer to perfect solid, even naming it to be fluid is misleading. It is not by chance that there are 'solid harmonics' for ones that might be familiar with it.
Biggest obstacle in science is not lack of knowledge but plain ignorance...
>regular and smooth kek
>>7653899
Jesus fucking Christ m8. You are trying waaaay too hard to sound smart. Many people care about this shit and, generally, they don't have that much trouble getting funding. Not any more than the rest of us, anyway.
Besides, if you really want to talk about NS being non-physical, why the fuck do you bring up black holes vs compressibility for fuck's sake? Come on man, all you need is a near-1 Mach velocities and all the incompressibility assumptions go right out of the window. And if you want to argue from more fundamental point of view even against compressible NS, there's a huge elephant in the room: infinite propagation of information.
You just sound like you have no idea what you are talking about mate.
>>7655296
Thanks for your feedback. I need to correct you, as I do not mean that NS is non-physical! NS was proven to be in many cases very good model for fluids. What I am referring to as an abstraction is incompressible fluid condition. If NS is mixed up with math in form of condition for incompressible fluid, representing an abstraction, one cannot rely that total outcome of math for NS representing reality and math for incompressible fluid representing abstraction. Such condition is not in alignment with having conservative vector field, as all solenoidal fields are non-conservative, therefore, blow-ups in math occur. On the other hand, I do not believe that reaching mach-1 has to anything with condition set for incompressible fluid, as it is exactly what it sounds like - incompressible, therefore, math making it to be such does not allow for anyting to be thrown away reaching any threshold, including mach-1.
Regarding elephant - not sure if I understand what you are referring to, however, as per my understanding of reality of nature, anything that is perceived as unlimited is at the same time abstract as well. Therefore, I do not believe that any infinite propagation of information is possible, regardless if 'infinite' referrers to speed of propagation of quantity of information propagated.
>>7655279
Hello! I wonder if you have any feedback and/or concern regarding pasted image?
>>7653756
Hallo! Thanks for your feedback regarding number of published articles on arXiv every day. That is fine, as none of those claim what is shared in linked document above. Truth is now out there. Regardless from where it gets into journal, if solution is correct, it will have to match what is documented in link provided above. Therefore, problem is solved and it could be as such ignored for very long time. However, it is just a question of time when somebody in academia will try to read and understand what is written. Once that happens, everybody will know the truth, which is inevitable.
>>7651800
Please note that link above:
navier-stokes.ateravis.com
now includes informal document summarizing vector fields for which valid solutions can (or cannot) exist.
engineer here. too lazy to read. gimme the formula i can plug and chug to make money.
OP is one of those really weird kids in your upper level math classes who literally thought he was a genius
he probably has really awful facial hair that he thinks makes him look cool for some reason, and/or his hairline is receding 10-20 years too early
Sorry to hear that OP
>>7655279
That would make it really smooth reading :-)
>>7651800
Did you notice youtube link on page 71 ?
http://youtu.be/ZXtoLbkfNYo
>>7651800
Did you use tikz to make those diagrams?
>>7653899
can you explain it even simpler ?
>>7651800
So first you try to explain stuff with pictures instead of math and then your first theorem is this obviously wrong statement.
Divergence freeness doesn't imply that the vector field is constant. For example magnetic fields are always divergence free yet magnets exist.
>>7656877
Absolutely agree. Gradient of harmonic functions is an good example when function is not zero, but is divergence free. However, for divergence condition for incompressible fluid, for solenoidal only fields which are also divergence free are not conservative- ie. do not conserve momentum/energy as required by NS. In order to be such and to align with conservation laws as well as to be incompressible fluid, solution is that velocity is constant or to accelerate everywhere equally. Maybe theorem statements needs to be refined in order to more clearly state context of incompressible fluids? I believe that is very good feedback as theorems might make wrong impression to be incorrect when first read. Thanks for your feedback!
>>7656772
Microsoft Visio is used for diagrams.
>>7656834
Yes, of course. The simplest intuitive explanation is that the universe of unlimited size, full of tightly packed ball bearings cannot behave like fluid. It is perfect solid, and whatever one might do to it (or not) it would simply not react -period.
>>7656344
>all these perosnal attacks for daring to share your ideas
Is there a law against this or something?
>>7656142
It is incorrect. You fail to grasp even basic undergrad mathematics! Amazing.
>>7653861
What I meant by 'shaky' is that, as >>7657537, I noticed that you managed to mess up the most basic rules of elementary algebra (for example, x^2 = y^2 does not imply x = y unless you can prove that x and y have the same sign) and make a very liberal use of the differential notation, which makes me doubt that you have a good command of real analysis, which in turn makes me doubt that you would manage to solve a PDE problem which is leaving the best analysts of the world stumped.
I *might* be wrong, but the overwhelming odds are that you are basing your reasoning on erroneous calculations.
>>7657560
Also, as I said, I did not see a math paper. I saw a lot of handwaving, calculations and no mathematical argument.
Can you sum up, in purely mathematical terms (ie. no physical mumbo jumbo) what it is that you proved in this paper and the main points of the strategy ? (ie. what should have been in your introduction)
>>7657577
In mathematical terms: its wrong. You don't apply the theorems correctly and thusly you are wrong. Stop being such a child by saying "hurr show me what I did wrong" when your fucking equations don't even follow from basic mathematics. Its equivalent so writing 1+1=3 and then saying non ironically "prove to me I'm wrong". You're fucking stupid, that's what's wrong.
>>7657599
>>7657599
Thanks for sincere feedback. I am wondering why would anyone get emotional about math. It is clear in case 1+1=3 what is wrong, but you cannot generalize things like that, as one could argue that what you said is like 1-1=2, so there you go, it is wrong. If you have explicit thing to point out, it would be appreciated. If required to make things more clear, I will do that, and refine those statements, as that is exactly why I posted document.
>>7657614
Exactly...some people gets emotional as it hurts to see things outside of the box.
>not using tensors
>think this is a proof
Wow what year is it? 1836?
>>7657560
Thanks! Where exactly you saw that? I need to check it out. In some situations, although math provides multiple solutions, it might not be physically reasonable to use negative values - i would have to validate context, but thanks for that, I will look into that.
>>7657560
You are probably referring to 4.9 to 4.10. I might need to explicitly state that scenario analyzed is in context of positive dx when fluid travels from x to x+dx, and that analysis for negative case would be identical analysis-wise. I was likely thinking that physical context and scenario of such directional fluid flow was obvious, but I might need to emphasize that.
>>7657772
Why tensors? It keeps one far from intuition, and one could imagine that anything is possible...cat in the hat, self replicating programs, and fluid to blow up...Such esoteric outcomes are much closer to witchcraft than science. Simpler-better.
>>7657849
Yes, but again this is supposed to be a math proof. There shouldn't be any physics in there. But it is not the only problem. At no point do you use any assumption on the function u, it is unclear what you're doing as your introduction doesn't state that clearly.
To see what I mean, here is an actual paper on Navier-Stokes http://arxiv.org/pdf/1307.6807v1.pdf
Note the thorough yet to-the-point introduction, the total lack of mention of the Clay institute, the presence of a plan of the proof and numerical tests, the absence of physics.
>>7657354
I didn't know Visio was capable of this. Neat.
>>7657945
Very useful suggestion! Thanks for that, as well as for the link to paper which I will carefully analyze. I clearly understand that it should be mathemathical proof, but I wonder why would one think that there should not be physics in there, as ask includes condition that states expectations related to 'physically reasonable solution'. I wonder what might be more physically reasonable then to assume that valid laws of physics, other than provided conditions, are satisfied? For sake of an illustrative example - if fluid has some density and mass, what is that supposed to mean other than plain vanilla understanding as per laws of physics? Otherwise, if anybody would have freedom to set mathematical statements expressing what means gravitational and what imans inertial mass and express all that nicely using math, what would be value of any prof completely detached from laws of physics and reality? If it is for sake of pure abstract exercise it might be fine, but I believe that the ask is that solution is 'physically reasonable' and not detached from laws of physics.
>>7657945
continuation from previous message:
NS itself is founded on laws of physics, which include what means pressure, conservation of energy, momentum, and balance between those in space and time for real physical system, and all of those are constructs of laws of physics.
I believe that big part of the overall issue is exactly in the fact that there are no formal mathematical mechanisms which are to be used to delineate between what in language of math represents reality supported by laws of physics, vs. some purely abstract math, which might be completely valid from mathematical point of view, but not having match in physical reality.
Based on my analysis, condition for fluid being incompressible is exactly that - an mathematical statement which does not have corresponding match in reality, and that is exactly where the issue is - once NS is used, which represents laws of physics, with something that does not, like condition for fluid to be incompressible, that is where things blow-up. NS is founded on conservation of momentum and energy, while solenoidal fields which are divergence-free are the opposite - not conservative and that is the essence of problem - mixing reality with pure abstraction as math describing reality (NS) cannot be mixed with math describing pure abstraction (incompressible fluid).
So far, everyone tried to find solution of NS or tried to prove that it does not work, taking condition of incompressible fluid for granted. It seems that nobody really looked in validity of incompressibility condition itself, which is exactly where is the problem and what I would like to share with everyone. If question is wrong, whichever way you try to answer it is not going to be correct. So the answer for this specific problem is that there is no solution as question is simply wrong due to incompressible fluid condition.
>>7657945
continuation from previous message:
Obviously, I appreciate very much support and suggestions from everyone via this forum and directly via e-mail, as it is obvious that writing papers is not really my 'bread and butter' kind of thing. However, I am quite sure that what I would like to share is correct, and I am hoping to find the best and most efficient way to express those perspectives in a way which are easily understandable and consumable.
>>7658035
> I wonder what might be more physically reasonable then to assume that valid laws of physics, other than provided conditions, are satisfied?
Because the problem is a mathematical problem. Of course, ideally the solution should conform to the laws of physics but the proof should still be mathematical (the conformity to the laws of physics is encoded in the statement of the problem).
That's a common way of doing things in PDE: You start by looking for what is called "weak solutions" (ie. distributions, maybe with some regularity) and then try to see if, among these, there are strong solutions (ie. continuous, differentiable functions) and, if you have more than one, *then* you may use a physical argument to discard the solutions you don't want.
>>7656548
You're not doing yourself any favors with these weird "Let it be" statements. It just looks like off-putting self-aggrandizing stuff to anyone who hasn't read the work.
>>7658054
Thanks for that suggestion - of course, I was not aware of that. I will need to think how best to do that in context of what I was previously referring to.
>>7658055
Noted. I will take it all out.
I thought that it might be entertaining to see something that can relate to first newton's law only - letting be & everything traveling in same speed as in that youtube video. I allowed myself freedom to try to look at things from lighter side and possibly expressing myself somewhat differently...bit different than 'same old', which might sparkle some new thoughts and ideas... It is interesting to hear how it is perceived, as my intention was not no 'aggrandize' myself- on the contrary as I would like to make myself least visible in order to avoid such perspectives and for people to focus on the subject, not the author... In whole scheme of things, author is not important at all - the truth is. I do not think that I would even take that prize as this is not about the prize. It is about truthfulness, open-mindness and open sharing of ideas.
>>7657772
>>7658739
Thanks for such sincere suggestion! I personally believe that nobody should be ignored, as behind the most vicious 'attack' there is rationale, which, putting emotions on side, in head of person writing it is definitely truthful. Therefore, one can learn a lot thinking about and understanding potential reasons for some outpours of emotional distress online in context of this discussion. In this particular case, I start to get impression that it is question of triggering potential embarrassment in the future as treat that you are referring to. Such embarrassment might be perceived as threat due to relative simplicity of rationale for this solution, which might be perceived as 'missed' by so many people dealing with it over decades in past. That is why solving this problem is difficult, as it is not only question of truth, but also overcoming perceptions of threat by solution which could be perceived as pointing to simple omissions not observed by so many intelligent people over many years. But, that is process which might take some time as it is important that everyone understand that it is not personal and just question of what is right. Meanwhile, I will try to cut clutter and refine what and how I wanted to say in formal way, as same thing could be presented in different ways from various angles and question is, which is the best one so that it maximizes understanding and minimizes perception of threat.
>>7658035
>I clearly understand that it should be mathemathical proof, but I wonder why would one think that there should not be physics in there, as ask includes condition that states expectations related to 'physically reasonable solution'.
The problem is:
>Prove or give a counter-example of the following statement:
>In three space dimensions and time, given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the Navier–Stokes equations.
There is nothing about being "physically reasonable". In the official statement of the problem, solutions have to satisfy certain technical details (the ones listed at the start of your document), but other than that, there are no restrictions.
>>7658739
continuation from previous message:
For example, Dr. Terrence Tao, extremely well known mathematician, one could say for very good reasons celebrity in mathematics worldwide and for which time many are competing , managed in 19 minutes and 49 seconds from the moment of original initiation of this topic to notice that something is posted, find time to review it, read and understand 80 pages document with math, conclude that it is wrong, and find time to write and communicate such conclusion with message not to further it anymore. It is very impressive performance! Dr. Tao, for some reason found that responding to this post is far more higher priority than reviewing articles of authors submissions to journals, which might take 3-6 months. In context when attempts of direct contact with Dr. Tao is ignored, one could find surprising lack of ignorance and vigilance for something as irrelevant as what I posted.
But, I am sure that Dr. Tao, as intelligent man, will eventually allow himself freedom to really think about what is in the essence of solution and recognize it as such, as truth cannot pretend not to be.
>>7658773
Here it is - please see captured image.
However, I understand what you want to say and point is taken. Thanks.
