The question of global regularity for the 3D incompressible Navier-Stokes equations remains one of the most profound open problems in mathematical fluid dynamics. In this paper, we introduce a novel geometric regularization mechanism, termed the ”Intrinsic Wrapping Constraint”, strictly bounding the topological volume of vortex stretching in R3. We reveal that this geometric bound is not an artificial construct, but a natural consequence of the Pressure Poisson Equation acting as an intrinsic topological back-reaction. Using weak formulation energy integrals, explicit Gagliardo-Nirenberg interpolations, and bounding the spectral eigenvalue λ via Gronwall’s inequality, we prove that the nonlinear vortex stretching term is strictly subordinated to the natural geometric damping. Furthermore, applying Bernstein-type inequalities to the bounded spectral phase-space ensures the pointwise vorticity ∥ω∥L∞ remains strictly finite for all time. Consequently, the BealeKato-Majda (BKM) criterion is rigorously satisfied, precluding any finite-time blow-up and ensuring global smooth solutions.
Efe SARICI (Sun,) studied this question.