4 ms·

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 spee

• eig 16d ago
  “ This is not the smoothness problem solution, but rather the Burgers vortex, an exact solution of the Navier–Stokes equations published by J. M. Burgers in 1948, chosen because it has the same anatomy: fluid drawn inward in a plane, stretched along the axis and thrown out of both ends, spinning fastest in a core.”
• pfortuny 16d ago
  It might be that the velocity at the spiraling axis is not infinity (i.e. there is no blow-up in finite time). Viscosity is a bitch.
  • chaostaco 15d ago
    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."
• chaostaco 15d ago
  I'm no expert in this field, but my understanding is that it would occur in the concentrating vortex core. The orange part would become narrower and narrower (the OpenAI article says "like spaghetti"), and the velocity in that concentrating region would grow without bound as the finite blowup time is approached. The rendered flow never literally shows "infinity" because every snapshot before the blowup time is still finite.