

This is still a big deal result with a lot of physical significance if it holds up.
Full Navier-Stokes are / were understood to model all of the important physics associated with continuous domain fluids. (Continuous domain here means we approximate the many, many particles of the fluid as a smooth, continuous substance).
In particular, Navier-Stokes are supposed to fully model fluids with turbulence. Turbulence is an everyday phenomenon that you can reproduce for yourself in your kitchen sink, and yet it is extremely difficult to formulate a mathematical function for it. Turbulence appears to be random if you look at it, and yet if it is produced by NS, then it is not random. Solving even the numeric approximations of NS for turbulent flows is difficult because the flows exhibit severe variation in velocity over wide ranges of time and distance scales.
Anyhow, if NS is a good physical theory it has to have a physically realistic solution to every physically-possible set of initial conditions and environmental forcing functions. In math terms this mainly means that all of the velocities, pressures, and forces have to be finite and smooth at all times. Step discontinuities don’t really occur in the real physical world (although they do approximately occur).
This result would mean that NS is not the end all final theory for classical continuum fluids. The scenario constructed by OpenAI is claimed to be one that can (at least theoretically) be setup and run in the real world. But if we did that, the real world is certain to do something else besides the infinite flow velocity vortex that OpenAI claims NS predicts. What would really happen in that experiment? Who knows. We’re gonna need to find some new physics to find out.













They did this to Houston, but they did an extremely half-assed job. It was one thin layer of additional asphalt covering over the whole intersection. But you can still see the pride crosswalk peeking out from underneath at the edges.
I’m still very upset.
Especially now that the sidewalks have been defaced with hate messages, which were then blacked out with spray paint. Is there a way to get the spray paint off the concrete and go back to chalk?