A Conditional Global Regularity Criterion for the 3D Navier–Stokes Equations via Subcritical Vorticity Stretching

We propose a conditional framework for global regularity of the three-dimensional Navier–Stokes equations based on a combined geometric and dissipative analysis of vorticity dynamics. The approach introduces a structured mechanism linking amplitude growth, temporal persistence, and dissipative cost through what we term a triple bridge principle. We show that global regularity follows under two conditions: (i) a dissipative thickness condition preventing supercritical spatial concentration of vorticity, and (ii) a subcritical bound on the effective positive vorticity stretching. The main contribution is the reduction of the global regularity problem to a precise condition on the vorticity stretching term. The validity of this condition remains open.