Another Millenium Problem May Have Been Solved

S3D writes "After recent verification of the proof of the Poincaré conjecture, another of the Clay Institute's Millenium Problems may have been solved. This new solution is for Navier-Stokes equations under physically reasonable conditions. Navier-Stocks equations describe the motion of fluid substances such as liquids and gases. Penny Smith has posted an Arxiv paper entitled 'Immortal Smooth Solution of the Three Space Dimensional Navier-Stokes System' which may prove the existence of such solutions."

Neat indeed

[Zx-man]

As a math major I may say the this is impressive: after understanding the significance and complexity of the problem seeing a solution has been found is really exciting. Although I'm looking forward to see something done about the most significant of the Millennium Problems (IMO and from the pure maths POV) -- the Riemann hypothesis [wikipedia.org].

Note: Not considering P vs. NP as it is quite possibly unprovable.

Someone had better tell the Formula One teams

[Simulacrus]

While I know they perform many, many computer simulations, I think aerodynamics is still regarded as one of the "black arts" in the field. Wind tunnels are still used extensively (it's often about who can build the better wind tunnel, never mind car). Maybe complete solutions of fluid movement will mean some odd-looking cars in 2007!

Re:It's the mathematics of ....

[thomasa]

Sorry, that is Catastrophe theory:

http://en.wikipedia.org/wiki/Catastrophe_theory [wikipedia.org]

Re:blink blink !

[the eric conspiracy]

I know some French, some Latin, and more math than either and have used the NS equation in my work (including nuerical slutions to subsets of the 3D problem). However ths would take me at least a couple of years of work to understand.

One of the things that I understood was a real problem with NS is that not only were there no existence proofs, but there were no uniqueness proofs. Does nayone know if the uniqueness question has been answered?

Re:Neat indeed

[ZorbaTHut]

That is true. However, note that unlike Godel's incompleteness theorem, P = NP has direct and obvious connections to the real world. We're not choosing between competing logical theories that exist in a vacuum. P = NP allows us to do certain interesting things on computers. If it turns out we can prove we'll never be able to do those, that is the same thing as saying it is impossible.

An arxiv article does not a headline make

[Wooster_UK]

Hmmm... the arxiv, of course, has a bit of a 'reputation'. They'll take anything, and more power to them for being willing to do so. However, it does tend to mean that if one's a non-specialist, the cranks can look awfully convincing. Without, obviously, wishing to ascribe that appellation to the good Associate Professor, I would note that this paper carries some of the hallmarks: an extremely dodgy abstract, poor punctuation (as described above in comments), ropey spelling, dubious use of English (whassiss "immortal"?) and poor LaTeX skills.

As I say, far be it from me to call "crank", but I'd wait for this to appear in a peer-reviewed journal and get responses. I suspect the Millennium (sp!) Prize committee may well be doing likewise.