
A scenario in which the Euler fluid equations fail - digital55
https://www.quantamagazine.org/mathematician-makes-euler-equations-blow-up-20191218/
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rcthompson
To cut through the not particularly helpful analogies, the core result (which
the article finally mentioned near the end) seems to be finding a situation
where the Euler equations work, but only for a finite time before hitting a
singularity. Previously, the only known cases either hit a singularity
immediately or never hit one, i.e. every case either works forever or doesn't
work at all.

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js8
I wonder if the illustration clip comes from this contraption by
SmarterEveryDay:
[https://www.youtube.com/watch?v=EVbdbVhzcM4](https://www.youtube.com/watch?v=EVbdbVhzcM4)

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kingbirdy
The attribution is from Shutterstock, so unlikely unless Destin uploaded it
there or someone stole his work.

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mechhacker
Off topic, but if you're interested in fluid simulations and want to learn
more about how they are actually made, John D Anderson's book on Computational
Fluid Dynamics is worth working through.

It's been quite some time but I remember going through it in Matlab to make
small, numerical simulations in the book.

The problem with fluids is that it's a very complex branch of physics with
many gotchas and many difficulties that you must navigate through, often
blindly, to get a reasonable approximation to a solution.

The fluids specialists I worked with on the past almost always needed actual
physical tests to prove out their engineered designs, rework simulations, etc.

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daxfohl
Does this lead to anything useful in the Navier-Stokes existence problem?

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iasuduisdf
I'll guess no, or that would have been the bigger story.

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daxfohl
Oh, true. And the article implies mathematicians were generally expecting this
result. But AFAIK there's not a strong consensus on which way the Navier-
Stokes problem will go. So probably unrelated techniques.

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Chris2048
The constant attempt to break this down into easier analogies make it more
confusing..

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fluffything
> They should be able to describe the motion of any fluid under any
> circumstances — and for more than two centuries, they have.

The Euler equations neglect viscosity.

> They also assume that fluids are “incompressible,” meaning that under the
> rules of the Euler equations, you can’t squeeze a fluid into a smaller space
> than the one it already occupies.

The Euler equations are compressible flow equations.

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These two mistakes could have been corrected had the author read the first
sentence of the wikipedia page about the Euler equations.

The TL;DR is that there are two papers that show that under many assumptions,
simplified versions of the Euler equations (which are already a big
simplification), blow up.

[https://arxiv.org/abs/1904.04795](https://arxiv.org/abs/1904.04795)
[https://arxiv.org/abs/1910.14071](https://arxiv.org/abs/1910.14071)

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iainmerrick
Thanks for toning down your attacks on the author! Although when you
completely rewrite your post after a couple of replies, it’s polite to note
that it’s been edited.

Your criticism is still incorrect. It’s true that there are both compressible
and incompressible forms of “the” Euler equations, but the papers you linked
to are very clear that they’re referring to the incompressible equations. The
abstract of the more recent one begins:

 _We study the stability of recently constructed self-similar blow-up
solutions to the incompressible Euler equation._

