Mathematics demigod Terry Tao came up with an extremely cool idea for how to prove blow-up results like this. https://www.youtube.com/watch?v=DgmuGqeRTto https:

Mathematics demigod Terry Tao came up with an extremely cool idea for how to prove blow-up results like this. https://www.youtube.com/watch?v=DgmuGqeRTto https://www.youtube.com/watch?v=DgmuGqeRTto. The idea is to try and make a self-replicating "fluid computer" - think of our imaginary fluid as a continuous set of points which are all moving independently. If you set things up in very particular way, you can treat patches of fluid like components in a machine - these interact with each other, moving energy around to different parts of the fluid, until eventually you end up with a new copy of the machine - but smaller - and with more average velocity than the original. This then repeats, smaller and smaller, faster and faster, until within a finite time you have a singularity. He used this to prove blow up in some 'toy' versions of the Euler equations, with extra rules / parameters to make it work, but he does (or did) seem to think this has some chance of working in the real model. (disclaimer - I do not have expertise in this field)