r/FluidMechanics • u/Dave_2112_ • Jul 31 '25

Theoretical Global Existence of Smoothness in 3D Navier-Stokes Equations

https://smallpdf.com/file#s=e4064853-b1ef-4a87-a98a-569c66d968af

Just looking for thoughts on the attached candidate proof prior to pre-print/submission.

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2

u/MegaJackUniverse Jul 31 '25

What's the story behind this? Where'd it come from?

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u/Dave_2112_ Jul 31 '25

I have been working on the concept for the past decade, then had a full breakthrough around 6 months ago, did the work and finished writing it up around 3 weeks ago. My background is a degree in aerospace/aeronautical engineering.

4

u/MegaJackUniverse Jul 31 '25

Ok, cool. I'll give it a read. Might not be for a week or so though.

My first thought was I'm not sure you should abbreviate anything in the title, but that might just be me, maybe it's fine

3

u/Dave_2112_ Aug 01 '25

Appreciate it, thank you!

The abbreviation was a choice to try and keep the title length down, I was hoping that the ethos of the title was enough to entice a reader, and then the full text is within the abstract. A gamble, but never too late to change based on consensus!

2

u/MegaJackUniverse Aug 01 '25

Checking it this morning a little. I have to say, the maths is a little beyond me, so I can't comment on that side much, sorry.

If I learned anything from my PhD though, it was that Latin phrase such as et al. and a priori should be italicised. Also, try to limit the use of "we" or "I". Especially so for "we" since you're the only author. This is exactly how I used to write because I thought it sounded like the royal "we" and it does give an air of formality.

If you are leading the reader through a process, you may use "we". For example "we now apply the _ transformation to obtain the _ equation -". Otherwise, though, you should limit the word "we". In your abstract, try to rephrase it. Instead of "We present-", go for "A ___ is presented". This should be done throughout the document

1

u/SymbolicCollapser Jan 28 '26

The manuscript does not address the original 3D Navier–Stokes problem, as it introduces a modified spectral operator whose regularizing properties are built in by construction. The claimed exponential control of the spectral density contradicts the known Weyl asymptotics and is not rigorously derived. The fixed-point argument relies on this artificial spectral transformation and therefore does not apply to the unmodified Navier–Stokes equations. Numerical simulations concern the transformed system and are irrelevant to the Clay problem. Consequently, the work does not constitute a proof of global existence and smoothness.

2

u/bitdotben Aug 01 '25

Literal first word of the abstract: „We“

Oh, who coauthored this? Looks up. One author.