Finite-time blowup

Interesting developments tonight, as Levent Alpöge and Tristan Buckmaster announce that after a fair amount of work they have constructed examples of finite-time blowup for a broad class of PDEs including 3-d incompressible Euler, inspired by of Diego Córdoba and Luis Martínez-Zoroa, and using plenty of LLM iteration in order to get the details right. This is, of course, a problem in the neighborhood of Navier-Stokes (in the negative direction of finding a counterexample to the conjecture, which I have over the years heard many PDE folks saying was the right way to bet), and Terry Tao says in a Mastodon thread that in principle this method doesn’t seem so far from showing blowup for Navier-Stokes too, though a large amount of compute and detail-checking would be involved. At least part of this has already been Lean-formalized, though perhaps eccentrically I find I care a little less about that. What matters is not whether there’s an example but whether the example has something to…