This is pretty, but none of those visualisations look very... singular to me? Can anyone tell me where to look in those simulations to see the blowup? Does speed go infinite in some region (which one? the blue or orange part?), or just non-smooth?
I believe a core element of the smoothness problem solution is that it does blow up in finite time, even with viscosity.
Perhaps an expert could provide a more accurate response, but here is how ChatGPT tried to explain it to me: "In this construction, the viscous term becomes large along with the acceleration, pressure-gradient, and nonlinear momentum-transfer terms, but they balance/cancel in a very precise way. That allows the velocity in the concentrating vortex core to grow without bound even though ν is nonzero."
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Perhaps an expert could provide a more accurate response, but here is how ChatGPT tried to explain it to me: "In this construction, the viscous term becomes large along with the acceleration, pressure-gradient, and nonlinear momentum-transfer terms, but they balance/cancel in a very precise way. That allows the velocity in the concentrating vortex core to grow without bound even though ν is nonzero."