• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,054 questions , 2,207 unanswered
5,345 answers , 22,721 comments
1,470 users with positive rep
818 active unimported users
More ...

  What is the New Look of Terence Tao at the Navier Stokes equations?

+ 7 like - 0 dislike

In a recent paper by Terence Tao (http://arxiv.org/abs/1402.0290), "Finite time blowup for an averaged three-dimensional Navier-Stokes equation," seems to suggest a new look on this problem.

I have briefly read through this commentator report: https://www.simonsfoundation.org/quanta/20140224-a-fluid-new-path-in-grand-math-challenge/.

I would like to probe to potential mathematical physcisits in this PO site,

What exactly is the new result or new thinking that Terence Tao provides in his paper? How relevant/important is this to solve the Millenium problem for Navier-Stokes equation?

add: There is also a very nice comment from Scott Aaronson http://www.scottaaronson.com/blog/?p=1697, who comments about the papers from L Susskind and T Tao, how their observations shade new lights on (classical or quantum) computations.

asked Apr 6, 2014 in Mathematics by wonderich (1,500 points) [ revision history ]
edited Apr 10, 2014 by wonderich

1 Answer

+ 9 like - 0 dislike

It's an approach for finding a counterexample, in case that smoothness fails. The idea is to find scaling-down blowups for Navier-Stokes type problems, so that a solution near his kind at scale A reproduces a very similar solution at scale A/2, and so on to A/4 until you get a singularity at a finite time. He has given a rather beautiful and nifty way of doing this construction in systems which are very similar formally to Navier Stokes, but modified so that he is able to control the reproduction process at each stage, and prove stability, so that little changes don't wreck his constructions.

The main thing about his method is that it requires that the fluid is actually capable of storing information stably for long enough to construct the next smaller stage, and this is likely false in the highly chaotic world of the turbulent systems, but who knows, it needs to be investigated thoroughly. Unlike other problems, Riemann Hypothesis, or Yang-Mills mass gap, this Clay problem we don't know the answer for sure, there might be a surprise.

If the solutions to Navier Stokes are actually smooth, which is more likely given present knowledge (although not certain), then his method will not solve the problem, rather they will work to exclude certain avenues of proof.

answered Apr 6, 2014 by Ron Maimon (7,720 points) [ no revision ]

Hm just from reading this nice answer, this systematic downscaling remotely reminds me of some kind of applying successive inverse RG transformations ... 

A very nice answer. Thank you, I hear your words. +1.

Ok, but please don't upvote too much, it's not a difficult answer.

There is also a very nice comment from Scott Aaronson: http://www.scottaaronson.com/blog/?p=1697, who comments about the papers from L Susskind and T Tao, how their observations shaded new lights on (classical or quantum) computation.

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights