@mathandcobb: What is... the Navier-Stokes equation, and what is the problem we are trying to solve? Here is an explanation of the equations, the problem, and what has been proposed as solutions #math #mathtok #differentialequations #navierstokes #fluiddynamics

Drb :

Do u think BSD conjecture will be solved soon?

EIAI :

There is a general misunderstanding that Navier Stokes equations are solved in the sense of being able to get a closed form solution to those equations, which is not the case and has never been a Millennium prize problem. What had been solved is a more theoretical questions like you described, which does not solve any real practical problems that fluid dynamics engineers are facing.

malekabozaid1 :

I always looked at Navier stokes equation as a great research topic and hoped one day I can get into the race but now its solved even before I took my bachelor's 😂

Sebastián Sierra :

with the current "solutions" found can we get closer to a stable relativistic version?

gdaymaytay :

why do mathematicians care about this, if the equations are non-relatavistic approximations to reality then why do mathemacians care if they can blow up?

marchesefulvio :

nice explanation

Zoomy :

what do you mean by smooth? i am not a mathematician.

sapiens.noeticus :

Why don’t mathematicians take open questions as a sign of broken math? It seems as if partial solutions are given more weight than they should.

davit_math :

Critical Audit of OpenAI's Navier–Stokes Proof: Scope of the Mathematical Audit, Independent Audit and Certification Status of the Lean Formalization, and Procedural Readiness for the Millennium Prize https://zenodo.org/records/22694089

AAAAAGHSH :

Finally someone who explains it well and non-sensationally 🤩 And yeah, from an engineering perspective the conditions described in that paper are so inapplicable to real fluid flows. Fluid Mechanics classes focus a lot on modelling assumptions and hence inherent limitations, and here the incompressibility assumption is not applicable considering that (iirc) the pressure field becomes extremely large as well. It would be interesting to use compressible NS (where you use slightly different conservation rules) to model the same scenario and see what happens.

esportsenthusiast :

for me u the goat

jedward :

Is the problem solved with any stronger conditions like for analytic functions or maybe using convexity assumptions?

Chemical kid :

I’ve solved the NS equation all the time. As long as we are in a symmetric coordinate system like cylindrical or spherical

no brain :

These are inviscid as I recall. Wouldnt the viscosity being present sufficiently regularize the solution?

ɔiɿɘᎸꙅoƚɒɿƚꙄ ɔiɿƎ :

cavitation has entered the chat

Fardarterfu :

So would an advancement then be a new equation that approximates without producing a singularity? Did we discover that NS is now certainly not the final say in modelling fluid dynamics?

UserHal9000 :

People, even in the math field, keep saying IA “solved” the navier-stokes equation… I have no idea why they believe that

Tzvi :

user5257148468125 :

What is the boundary of the theory trying to tell you? Listen carefully.

Mason :

Nice explanation!

jam :

Is there a quantum mechanics version of navier stokes ?

Ben1131 :

👌👌👌