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## #1 2006-10-06 23:45:26

MathsIsFun
Registered: 2005-01-21
Posts: 7,660

### Navier-Stokes (A Millenium Problem) Solved?

Apparently Professor Penny Smith of Lehigh University has a solution to the Navier-Stokes equations.

If true, this will not only earn a 1 Million Dollar prize from the Clay Institute, but will make it a lot easier to solve problems in Fluid Mechanics, which will benefit all kinds of things, such as boats, planes, cars, weather prediction and more.

A good blog on this is: http://scienceblogs.com/goodmath/2006/10/navierstokes_another_historic_1.php

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #2 2006-10-07 08:13:13

simron
Real Member
Registered: 2006-10-07
Posts: 237

### Re: Navier-Stokes (A Millenium Problem) Solved?

What are the Navier-Stokes equations?

Linux FTW

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## #3 2006-10-07 08:21:34

Patrick
Real Member
Registered: 2006-02-24
Posts: 1,005

### Re: Navier-Stokes (A Millenium Problem) Solved?

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## #4 2006-10-07 10:39:20

MathsIsFun
Registered: 2005-01-21
Posts: 7,660

### Re: Navier-Stokes (A Millenium Problem) Solved?

Also: http://en.wikipedia.org/wiki/Navier-Stokes

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #5 2006-10-07 11:45:28

mikau
Member
Registered: 2005-08-22
Posts: 1,504

### Re: Navier-Stokes (A Millenium Problem) Solved?

Basicly what she did was find a solution to a never before solved differential equation.

I was suprised to find out it was a girl that did it. Remarkable! I didn't know ANY girls liked math! lol..but seriously, how many math theorems were actually created by women? Its a pity more girls don't like math. Who knows? Maybe some problems just require a womans touch to solve!

A logarithm is just a misspelled algorithm.

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## #6 2006-10-07 12:45:53

polylog
Member
Registered: 2006-09-28
Posts: 162

### Re: Navier-Stokes (A Millenium Problem) Solved?

It seems like the paper proves the *existence of a solution*, more specifically the existence of an 'immortal smooth solution' (whatever that is)... is this enough for the prize?

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## #7 2006-10-07 12:56:04

polylog
Member
Registered: 2006-09-28
Posts: 162

### Re: Navier-Stokes (A Millenium Problem) Solved?

Ok reading the problem stament it seems that is what the prize requires! Awesome.

However, its a bit confusing, as it seems the equation is not actually solved -- it's a proof of the existence of smooth solutions -- does this actually help in practical applications?

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## #8 2006-10-09 05:18:23

cray
Member
Registered: 2006-10-05
Posts: 29

### Re: Navier-Stokes (A Millenium Problem) Solved?

It may sound like a trivial comment to some or most people, but I can see that it will also have implications in advanced computer games and simulations. The object of which is usualy to provide a more realistic virtual experience.

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## #9 2006-10-09 10:19:00

polylog
Member
Registered: 2006-09-28
Posts: 162

### Re: Navier-Stokes (A Millenium Problem) Solved?

The author has withdrawn the solution !!

http://motls.blogspot.com/2006/10/immortal-smooth-solution-withdrawn.html

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## #10 2006-10-09 22:44:06

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Navier-Stokes (A Millenium Problem) Solved?

Ah, that's a shame. No million dollars for her.

Still, it's possible that she can just tweak her current proof a bit to make it work properly. She probably won't have to start completely again.

Why did the vector cross the road?
It wanted to be normal.

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## #11 2006-10-10 04:56:03

cray
Member
Registered: 2006-10-05
Posts: 29

### Re: Navier-Stokes (A Millenium Problem) Solved?

Why doesnt she just ask the people who designed 3DSMax and Maya, or Lightwave?, They have been solving that stuff for years

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## #12 2006-10-10 05:18:24

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Navier-Stokes (A Millenium Problem) Solved?

I'd imagine that those people would use approximations in order to simplify the maths of it, whereas she wants to find the exact answer.

Why did the vector cross the road?
It wanted to be normal.

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## #13 2006-10-19 03:41:20

mikau
Member
Registered: 2005-08-22
Posts: 1,504

### Re: Navier-Stokes (A Millenium Problem) Solved?

and supposedly the approximations are pretty time consuming. A formula for the exact answer would most likely be faster, and more accurate.

A logarithm is just a misspelled algorithm.

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## #14 2006-10-19 09:31:19

MathsIsFun
Registered: 2005-01-21
Posts: 7,660

### Re: Navier-Stokes (A Millenium Problem) Solved?

What a pity she wasn't right, but she may have pointed the way.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #15 2006-10-19 10:44:39

Patrick
Real Member
Registered: 2006-02-24
Posts: 1,005

### Re: Navier-Stokes (A Millenium Problem) Solved?

I thought about this topic when I saw the news the other day. There was a danish, female, professor. Believe it or not, it was another Professor Smith. A female professor called Smith, what are the odds?

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## #16 2006-10-19 15:23:48

MathsIsFun
Registered: 2005-01-21
Posts: 7,660

### Re: Navier-Stokes (A Millenium Problem) Solved?

The odds are:

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #17 2006-10-19 17:42:25

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

### Re: Navier-Stokes (A Millenium Problem) Solved?

MathsIsFun wrote:

The odds are: