Navier-Stokes (A Millenium Problem) Solved?

MathsIsFun · 2006-10-06 23:45:26

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

simron · 2006-10-07 08:13:13

What are the Navier-Stokes equations?

Patrick · 2006-10-07 08:21:34

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

MathsIsFun · 2006-10-07 10:39:20

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

mikau · 2006-10-07 11:45:28

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!

polylog · 2006-10-07 12:45:53

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?

polylog · 2006-10-07 12:56:04

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?

cray · 2006-10-09 05:18:23

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.

polylog · 2006-10-09 10:19:00

The author has withdrawn the solution !!

http://motls.blogspot.com/2006/10/immortal-smooth-solution-withdrawn.html

mathsyperson · 2006-10-09 22:44:06

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.

cray · 2006-10-10 04:56:03

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

mathsyperson · 2006-10-10 05:18:24

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.

mikau · 2006-10-19 03:41:20

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

MathsIsFun · 2006-10-19 09:31:19

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.

Patrick · 2006-10-19 10:44:39

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?

MathsIsFun · 2006-10-19 15:23:48

The odds are:

or thereabouts.

luca-deltodesco · 2006-10-19 17:42:25

MathsIsFun wrote:

The odds are:
or thereabouts.

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

Math Is Fun Forum

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

Navier-Stokes (A Millenium Problem) Solved?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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