Here is a link(which contains other links) which you will find interesting. It appears a math professor at Lehigh University may have solved the Navier-Stokes PDE's regarding viscosity. Check it out.
MMB
Not a he, a she. Professor Penny Smith from Lehigh University. Follow the link to her paper. It was just recently submitted, I believe. It'll have to survive scrutiny by the muckity-mucks who are qualified to judge it.
[math/0609740] Immortal Smooth Solution of the Three Space Dimensional Navier-Stokes System
Smith's Navier-Stokes
I know absolutely nothing about it (though heard of it). Thus, I might be completly off. But it makes no sense to say he proved existence of solution. Because Differencial equation always have solutions on continous open intervals.
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Does Wikipedia mention it?
If not, it is probably wrong.
Like I said, people love to make false proves on website based on no understanding at all.
I have faith in Wikipedia, PlanetMath, MathWorld, MacTutor.
Because these are website that are checked.
I have absolutely no faith in regular website that people make themselves. Because I have seen so mannny mistakes.
Especially people claiming they have proofs and knowing almost no math.
I would say the same for non-math related things. You can check regular sites. But if they say something interesting/shocking you need to confirm this from a trusted website.
The introduction to the paper in the original link claims that the existance for solutions in 3-D hadn't been proven. The Navier-Stokes equation is a 3-D non-linear system of equations (one for each coordinate). Being non-linear I don't know if a solution has to exist. Obviously approximate and/or local solutions exist else fluid dynamics never would have been developed.
-Dan
Why are these called "Mellenium Problems".
They are not so old.
There are only 2 real mellinium problem from the time of Euclid (more than 2300 years ago). Twin Prime conjecture. And the dangerousOdd Perfect Number
I think there is one most from the time of Pythagorus (more than 2500 years ago). I do not know who it is called, and I do not really know if it is unsolved. But I think it is. Show there is not thing as a slightly excessive number. Meaning when you add the proper divisors you obtain a number 1 more than the number you used. If what I said is true, this is the oldest unsolved problem.
It happens to be cool that the most complicated math problems involve the most basic things, the positive integers. Funny, all of these advanced PDE's eventually are solved after a some time. But these problems, which a child can understand still unsolved. Even by the greatest mathemations.
Also read about it here:
Brooks Moses: Notes on Divergent Simulations » Penny Smith’s Proof on the Navier-Stokes Equations
and
http://www.nature.com/news/2006/0610...061002-14.html
This isn't made up. It's the real deal. Now, we'll see if her proof stands the 2 years required scrutiny to claim the prize.
Dr. Penelope Smith(currently on leave) is Associate Professor of Mathematics at Lehigh University in Bethlehem, PA. She earned her PhD from Polytechnic Institute of Brooklyn. Her specialties are Differential Geometry and Geometric Measure theory
There are seven unsolved problems that are properly labeled "The Millenium Problems". They were instated by the Clay Mathematical Institute, so we don't really have a choice as to which ones they will be. A quote from the lecture:
"A prize of $1 million will be awarded to the person or persons who first solved any one of seven of the most difficult open problems of mathematics."
These problems are:
- The Riemann Hypothesis
- Yang-Mills Theory and the Mass Gap Hypothesis
- The P vs. NP Problem
- The Navier-Stokes Equations
- The Poincare Conjecture
- The Birch and Swinnerton-Dyer Conjecture
- The Hodge Conjecture