The Navier-Stokes equations are supercritical, meaning that at smaller scales, the transport terms dominate over the viscosity terms, leading to unpredictable and turbulent behavior.

The Navier-Stokes equations govern fluid flow for incompressible fluids like water, and the Navier-Stokes regularity problem asks whether a smooth velocity field can ever concentrate to the point of becoming infinite, which would indicate a singularity.

Grigori Perelman transformed the supercritical Navier-Stokes problem into a critical problem by introducing concepts like reduced volume and permanence entropy, which simplified the analysis of singularities.

The Clay Foundation offers a million-dollar prize for solving one of the seven Millennium Prize Problems, one of which is the Navier-Stokes problem, and only one of these problems has been solved so far.

Mathematicians care about whether something holds true 100% of the time, unlike most fields where 99.99% suffices. This is crucial in fluid dynamics, where we need to understand if there are special initial states that could lead to blow-up scenarios.

Maxwell's equations are conformally invariant, meaning they depend on the space-time structure independent of scaling.

The concept of twistors introduces a new kind of curved twistor, which is essential for understanding complex solutions in physics, but it also leads to inherent confusion in the theory.

Through engineering, we can create clever constructions that lead to interesting behaviors in fluid dynamics, similar to how glider guns and gates operate in the Game of Life.

The phenomenon of supercriticality versus criticality and subcriticality is a key qualitative feature that distinguishes equations that are predictable from those that are not, such as in fluid dynamics.