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#1 2006-10-07 21:45:26

MathsIsFun
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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


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#2 2006-10-08 06:13:13

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

What are the Navier-Stokes equations?


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#3 2006-10-08 06:21:34

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

The provided link will tell you what it's about...


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#4 2006-10-08 08:39:20

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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
 

#5 2006-10-08 09:45:28

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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!


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#6 2006-10-08 10:45:53

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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?

 

#7 2006-10-08 10:56:04

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

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

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?

 

#8 2006-10-10 03:18:23

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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.

 

#9 2006-10-10 08:19:00

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

The author has withdrawn the solution !! sad

http://motls.blogspot.com/2006/10/immortal-smooth-solution-withdrawn.html

 

#10 2006-10-10 20:44:06

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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.


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#11 2006-10-11 02:56:03

cray
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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

 

#12 2006-10-11 03:18:24

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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.


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#13 2006-10-20 01:41:20

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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.


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#14 2006-10-20 07:31:19

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

And knowing an exact answer could lead on to other breakthroughs!

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
 

#15 2006-10-20 08:44:39

Patrick
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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 2006-10-20 13:23:48

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

The odds are:



or thereabouts.


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#17 2006-10-20 15:42:25

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

MathsIsFun wrote:

The odds are:



or thereabouts.

at an improbability factor 1.2456 to the power of negative 10000! my my.


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