The Navier–Stokes Existence and Smoothness Problem and the Principle of Feedback and Scale Barrier

This study presents a demonstration of the Navier–Stokes existence and smoothness problem, which asks whether, in three dimensions, an initially regular fluid can develop a singularity in finite time. The approach is based on the Principle of Feedback and Scale Barrier. It shows that the contraction of a structure toward smaller scales simultaneously strengthens the action of viscous diffusion, leading to a limiting feedback and a critical scale barrier that prevents progression toward zero scale.