The Million-Dollar Question: A Primer on Regularity

Deep End Era. Engineering with Sankalp · Oct 12, 2026 · 50m

Farah watches her daughter spin on the ice and asks what stops a fluid's vortex tubes from spinning up forever. The episode covers the vorticity equation (stretching, carrying, diffusing) and why stretching vanishes in 2D; axisymmetric flows with and without swirl; the cascade as vortex stretching; the Burgers vortex balance; and Leray's lower bound on blowup speed. Beale-Kato-Majda turns blowup into one quantity to watch. Caffarelli-Kohn-Nirenberg partial regularity, which Fefferman calls the best known, allows isolated points but no moving singularities. ESS closes the L-three endpoint…