« 2006 Nobel Prize in Physics
November Notices »

Navier-Stokes Problem Solved?

October 5th, 2006 by Walt

Penny Smith has posted a preprint to arXiv, Immortal Smooth Solution of the Three Space Dimensional Navier-Stokes System that, if correct, would solve one of the Clay Institute’s Millenium Problems. Christina Sormani has created detailed summary of Smith’s work on PDEs and Navier-Stokes.

The Navier-Stokes equation is a set of equations that describe fluid flow in Newtonian mechanics. The equations are notoriously difficult to analyze. The existence of smooth solutions for all time (the meaning of “immortal” in the paper title) has long been an open question. One now perhaps closed.

Via Peter Woit.

Update. The paper has been withdrawn. (Via John Baez in the comments.)

This entry was posted on Thursday, October 5th, 2006 at 11:19 pm and is filed under Mathematics, Physics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

3 Responses to “Navier-Stokes Problem Solved?”

  1. Memories of a Weird Traveller » Blog Archive » Progress in the Navier-Stokes problem? Says:
    October 6th, 2006 at 1:28 am

    [...] Via Ars Mathematica: [...]

  2. John C. Baez Says:
    October 8th, 2006 at 2:03 pm

    Penny Smith has withdrawn her paper claiming to prove global-in-time existence of solutions for the Navier-Stokes equation, citing a “serious flaw”. Try the remarks by “Euler” on Peter Woit’s blog for more details.

  3. Walt Says:
    October 8th, 2006 at 3:45 pm

    I updated the post accordingly.

    Euler’s point about the theorem apparently applying to Burger’s equation was a good one, but I didn’t check the preprint to see if it was really right.

Leave a Reply