Description This work identifies a necessary condition for finite-time singularity in the three-dimensional incompressible Navier-Stokes equations expressed in terms of vorticity. By analyzing the vorticity equation, we isolate vorticity stretching as the sole amplification mechanism and show that any blow-up must be accompanied by divergence of the cumulative cubic vorticity integral: int₀T* int |omega|³ dx dt This provides a precise formulation of the amplification requirement underlying singularity formation and reduces the problem to control of a single spacetime quantity. The result is consistent with known continuation criteria and situates cubic vorticity as a natural candidate for further analysis. The sufficiency of this condition remains open.
Vasconcelos Antonio Jorge (Tue,) studied this question.