Global Finite-Time Blowup Solutions to the 3D Navier–Stokes Equations via Initial Vorticity Contrast

This paper investigates the global finite-time blowup problem of smooth solutions for the three-dimensional incompressible Navier–Stokes equations. We construct a class of divergence-free, compactly supported smooth initial velocity fields with intrinsic spatial vorticity contrast. By establishing uniform persistence of vorticity spatial discrepancy via rigorous contradiction arguments and localized integral estimates of vortex stretch ing, boundary transport and viscous dissipation, we derive a modified Riccati-type differential inequality with explicit viscous damping terms for the vorticity magnitude functional. Under the standard BKM (Beale–Kato–Majda) blowup criterion, we prove that the constructed initial fields generate solutions that develop global finite-time sin gularity in the vorticity field. This work only confirms the existence of finite-time blowup paths and does not deny the global regularity of solutions for other admissible initial data. All derivations follow rigorous analytical frameworks without redundant empirical assumptions。