Chris Combs, professor of Aerospace engineering, throws some cold water on OpenAI’s NS solution

“Some thoughts on the Navier-Stokes news from a professor of aerospace engineering: 1) take a deep breath 2) posts indicating we "solved Navier-Stokes" are incorrect and overblown. A very specific mathematical proof involving a niche scenario for Navier-Stokes has *potentially* been shown (that a perfectly smooth incompressible initial condition with finite energy could produce a singularity--note the assumptions here piled on to an equation set that already involves some assumptions). 3) there is no general closed form solution for N-S and that's not what this news is about 4) this is more of a mathematical curiosity than anything else and could matter a lot to mathematicians but basically changes nothing in the way N-S are used in practice 5) there are already very useful exact solutions to Navier-Stokes that greatly simplify the equation set with the right boundary conditions/geometry like laminar flow through a pipe or a 2D Taylor-Green vortex 6) in aerospace, we already treat N-S as an approximation in many instances and are well aware of its limitations. we don't outright solve these equations anyway and regularly chop off terms or simplify parts (at the expense of accuracy) to make them easier to deal with. 7) to be honest I have never found this specific problem to be particularly interesting because we know a core assumption of N-S is a "continuum" fluid where you ignore molecules and assume hydrodynamic scales >>> molecular scales. We know a real fluid cannot have infinite velocity or energy. But clearly you can push equations outside of their bound of validity and make them produce funky results and singularities.” https://x.com/drchriscombs/status/2097409234321154547?s=46