The Navier-Stokes Equations in your coffee #science

[gsharpenmydjencil]

“Deceptively easy” …
Lady…. Idk what half of those shapes mean

[davidgillies]

The problem isn't to "prove" the Navier-Stokes equations; it's to demonstrate the _existence_ of certain solutions (or to provide a counterexample thereof); specifically that there exist globally defined functions in R^3 that are smooth and divergence-free which satisfy the equations.

[TheMotlias]

Forget the millennium prize money, there are companies who will pay way more than a million for the maths to accurately simulate fluids

[jamiehelm]

This brings back horrid memories of aerodynamic theory classes where we were modeling a single molecules path over a wing in a 2d model. I seem to remember pages and pages of calculations for a single point plot….god knows what that would be in 3d. Maybe advances in FEA can do this now?

[t.jefferson]

My brain just broke. Imma get some cocoa and a blankie now.

[brendandwyer]

I'd be Stoked to understand any of what you just said

[OL]

Rhe prize is not even for solving the equations but "only" to hard-prove some of their already known properties we desperately want them to be always true but we can't prove. Thes equations are true monsters nobody will ever tame!

[queefyg]

The Navier Stokes equations are a system of differential equations, we know solutions in certain cases and we even use this with computers to model fluid flow in a simulation, to win 1 million dollars you need to show that a particular set of solutions exists, it's weird as fuck to think about but this is usually the case with non linear DE.

[kayenrexzo.]

Just for clarity, those are Navier-Stokes equations for ρ = const., right? If I remember correctly, then div(v) = 0 comes from the continuity equation, that would typically have a second term including the time derivative of density.

[wedot]

This is very interesting. The one poster above that posted about aerodynamics class was probably the closest.

These equations don't necessarily need to be solved. Basically they describe energy, momentum, and continuity, over a control area, or control volume.

So while they don't get solved like y = mx + b might, this video is correct that The system solution is incredibly sensitive to the starting conditions.

[TrancorWD]

It's funny how much Navier-Stokes is used in 3d graphics for fluid/volume sims all the way to crowd/boid simulations.
I've taken strongly from Navier-Stokes over my career, yet it's unsolved; so useful in so many ways.

[vasaaviarion]

I have a masters in Physics. Ive been reattempting this problem for years. It is indeed, extremely hard

[newpotential]

Just triggered ptsd from my Fluid Mechanics coarse.

[-crusader]

“Deceptively easy” I learned those symbols a week ago, that isn’t easy by any stretch of the imagination

[jumpanama]

I'm an aerospace engineer and have a book titled "An Introduction to the Mathematical Theory of the Navier-Stokes Equations" and the very first page has the full partial differential equation form of the NS in steady state. That's just an introductory book and the first page is that...

[lucas____________]

You don’t need to solve them, people ‘solve’ them all the time with simplifying assumptions. You need to prove the existence or non existence of a general solution and its smoothness, which basically means you don’t have jump changes in values.

[adolphgracius]

That's the equivalent of saying if you can solve world hunger I will give you 10K

[travisderksen]

The answer is 42











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[----I...have...no...clue....]

The unified theory was solved in 1971, when Marvin Gaye sang "Everything is Everything".

[mybetterhalf]

That makes the mess in my garage a fluid....🤣🤣