This preprint investigates the finite-time blow-up problem for suitable weak solutions of the three-dimensional incompressible Navier–Stokes equations. Assuming the existence of a finite-time singularity, the analysis is reduced to a scale-normalized critical configuration. A structural dichotomy between coherent and mixing regimes of the vorticity is established. In both regimes, a quantitative absorption mechanism yields an ε-improvement at smaller scales. Iteration of this mechanism contradicts scale-criticality, thereby excluding finite-time singularities within the considered framework. The results provide a structural obstruction to sustained self-accelerating vortex stretching and contribute to the global regularity problem from a scale-critical perspective.
Simita Roland (Tue,) studied this question.