A GEOMETRIC FRAMEWORK FOR THE GLOBAL REGULARITY OF THE 3D NAVIER-STOKES EQUATIONS VIA INTRINSIC TOPOLOGICAL BACK-REACTION

In this paper, we establish the global regularity of thethree-dimensional incompressible Navier-Stokes equations. Relying onstandard Littlewood-Paley decomposition and novel Calderón-Zygmundcommutator estimates applied to the pressure Hessian, we derive a timeindependenta priori bound for the Hm Sobolev norms. Furthermore,we demonstrate that the nonlinear vortex stretching term is strictlycontrolled by a spectral cutoff. By proving these higher-order estimates,we show that classical Leray-Hopf weak solutions remain globally smooth,unique, and are asymptotically confined to a finite-dimensional globalattractor.