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Another Clay Institute Millenium Prize Problem Solved?
October 5, 2006 6:28 AM   Subscribe

The Navier-Stokes equations constitute the fundamental equations that describe fluid mechanics, and are used everywhere from atmospheric science to airplane design. Proof of the existence of a smooth solution to the Navier-Stokes equations in 3-dimensions is considered a challenging problem, so challenging that the Clay Math Institute has offered a million dollars to anyone who can do so. Has it been done? (More detailed explanation). (via)
posted by onalark (17 comments total) 3 users marked this as a favorite

 
Wow. What a spectacular time for mathematics.

(As a tiny bit of added spice, note that the "More detailed explanation" link is by Christina Sormani, who was a postdoc with Shing-Tung Yau, recently in the news. I don't know Sormani, but I tend to trust her description of Smith's work, just based on reputation.)
posted by gleuschk at 7:24 AM on October 5, 2006


Oh my. Oh my indeed. Can this really be true?
posted by vernondalhart at 7:29 AM on October 5, 2006


Can epimorph please let me know whether the author is full of it? But I guess will find out soon enough, as I'm sure every scholar of real analysis is pouring over this as we speak.
posted by noble_rot at 8:16 AM on October 5, 2006


Wow. This would be very, very big.
posted by mr_roboto at 11:20 AM on October 5, 2006


That's pretty damn impressive. I thought that the equation was actually proven to be unsolvable.
posted by delmoi at 11:27 AM on October 5, 2006


no way!! first the Poincaré Conjecture and now this. odds that someone finds a flaw in her proof? anybody intimate with state of the art in PDEs?
posted by jcruelty at 3:31 PM on October 5, 2006


I consider it one of my lifetime crowning acheivements that I managed to understand the Navier-Stokes equations enough to get my aerospace engineering degree. A degree which turned out to be useless for me*, but hey it's fun to point to sometimes. Not that I remember any of that stuff, mind you ...

Gawd, that LaTex look in the paper is so HOT. Written by a woman. I'm about to swoon.

* Hey, YOU try to get an AE job during the post Cold War defense contraction period in the early 90s while competing against laid-off Rockwell guys with 35 years of experience. Oh and I had a 2.4 GPA. Woooooo!
posted by intermod at 8:06 PM on October 5, 2006


Gawd, that LaTex look in the paper is so HOT.

LaTex is nerd-speak for "Hey, check out my Big Brain!"
posted by spazzm at 4:49 AM on October 6, 2006


Does this mean I can go back and complain to my aerodynamics professor now?
posted by casarkos at 6:36 AM on October 6, 2006


i haven't seen any updates... what's the dilly?
posted by jcruelty at 11:51 AM on October 6, 2006


i haven't seen any updates... what's the dilly?

The 'dilly', my friend, is that mathematics professors highly trained in this field will be pouring over her research for years before a decision is made. Although her proof is 9 pages, this is the final link in probably more than a decade's worth of work for her (as evidenced by all the referenced publications).
posted by onalark at 1:59 PM on October 6, 2006


I got a pleasant note from Christina Sormani, asking me to make sure two things are clear:

1. She hasn't claimed to have checked Smith's work on the webpage linked in the post, just to provide an exposition which will help those involved in the verification process (which will likely take years).

2. She was a postdoc with S.-T. Yau back in the 90s, and is now on the faculty at CUNY.

It's "poring", not "pouring".
posted by gleuschk at 7:40 AM on October 7, 2006


The paper has been withdrawn.
posted by gleuschk at 3:59 PM on October 8, 2006 [1 favorite]


Thanks for the update gleuschk.
posted by onalark at 9:29 AM on October 9, 2006


One of my analysis friends said something about one of her results leading to a contradiction, so there's some sort of discrepancy in her proof (which would explain the withdrawl). Well it was a good bit of excitement anyway, and I'm hoping she'll be able to correct the error.
posted by onalark at 6:21 PM on October 9, 2006


There's a fair amount of new information on Christina Sormani's page linked in the original post.

The surprising thing about the retraction is that the error was found in one of Smith's papers that had already been refereed, accepted for publication, and had even appeared in print. That sort of thing isn't supposed to happen. Generally speaking, the author always holds the final responsibility for the correctness of his/her results, but if I were the referee for the previous paper, I'd be pretty damn embarrassed about now.
posted by gleuschk at 5:58 AM on October 10, 2006


There's some followup about the withdrawal in this SlashDot post -- 4th item down.
posted by intermod at 5:50 AM on October 27, 2006


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