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Comment by fluffything | Hacker News Reader

> 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/1910.14071

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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.

Don’t be silly. You’re leaping from nitpicking to a blanket assumption that the author is completely clueless.

Elsewhere in the article: The Euler equations are not a literal description of a real-world fluid. They include several nonphysical assumptions.

The author does in fact know about the subject.

Further down in this article, Kevin Hartnett wrote:

> The Euler equations are not a literal description of a real-world fluid. They include several nonphysical assumptions. For example, the equations only work if internal currents within a fluid don’t generate friction as they move past each other. 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. > [...] > These unnatural provisos led the mathematician and physicist John von Neumann to quip that the equations model “dry water.” To model the motion of a more realistic fluid with internal friction (or viscosity), researchers use the Navier-Stokes equations instead.

So it seems they know what they are writing about, at least more than you supposed.

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