> One of the central problems in fluid dynamics is to figure out if the [Euler] equations ever fail, outputting nonsensical values that render them unable to predict a fluid’s future states.
> Mathematicians have long suspected that there exist initial conditions that cause the equations to break down. But they haven’t been able to prove it.
> In a preprint posted online last month, a pair of mathematicians has shown that a particular version of the Euler equations does indeed sometimes fail.
...
> Perhaps in some situations, the equations will proceed as expected, producing precise values for the state of the fluid at any given moment, only for one of those values to suddenly skyrocket to infinity. At that point, the Euler equations are said to give rise to a “singularity” — or, more dramatically, to “blow up.”
> Once they hit that singularity, the equations will no longer be able to compute the fluid’s flow.
...

Computer Proof ‘Blows Up’ Centuries-Old Fluid Equations
https://www.quantamagazine.org/computer-helps-prove-long-sought-fluid-equation-singularity-20221116/

Very important and interesting work, if you're a mathematician, a physicist or an engineer that has ever 'crashed' with Euler/Navier-Stokes equations.

#math #physics #fluids #euler #navierstokes #equations #singularities