[rossant]

They are building a formally-defined counter example to this? Am I understanding correctly?

> In three space dimensions and time, given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the Navier–Stokes equations.

[hodgehog11]

They find a very good approximate blowup solution (non-smooth) using a NN. When the solution is good enough, you just need careful fixed point theory to infer an actual solution.