Terence Tao finds finite-time blowup for an averaged 3D Navier-Stokes equation
Finite time blowup for an averaged three-dimensional Navier-Stokes equation
Terence Tao has posted a paper that formalizes the 'supercriticality barrier' for the Navier-Stokes global regularity problem. He constructs an averaged version of the Navier-Stokes nonlinearity that satisfies the same energy identity and function space estimates as the true equation, yet admits solutions that blow up in finite time. This is the first such blowup result in three dimensions that respects the energy identity. The proof hints at a possible route to blowup for the actual Navier-Stokes equations.
Intriguingly, the method of proof in fact hints at a possible route to establishing blowup for the true Navier-Stokes equations, which I am now increasingly inclined to believe is the case (albeit for a very small set of initial data).
- v64
This is going around due to rumors and baseless speculation on Twitter [1] right now that Anthropic has solved the Millennium problem related to Navier-Stokes [2]
[1] https://x.com/AndrewCurran_/status/2096062392442724805 for example
[2] https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existenc...
- goldenarm
@dang please can we add a [2014] to the title ?
- tacomonstrous
This is essentially irrelevant to the content of the post, but it's amusing to me that he casually mentions submitting to JAMS as if its acceptance were a mere formality.
- MeteorMarc
See https://www.quantamagazine.org/theory-of-fluids-enters-the-2... if you want to know what the Navier Stokes equations are about.
- immmmmm
It’s pretty crazy what dynamics you get from NS.. until one realise they emerge from a tiny part of the solution space of Einstein equations.. which themselves emerge at the low energy limit of sth much bigger.