RETRACTED: A Geometric Constraint Framework for Global Regularity of the 3D Navier-stokes Equations

Abstract

Abstract

We propose a new framework for addressing the global regularity of the three dimensional incompressible Navier-Stokes equations. At the core of our approach is a geometric constraint on the dynamics of the vorticity and velocity gradients that prevents the concentration of energy at arbitrarily small scales. We formalize this constraint globally and locally, integrate it with scale-by-scale control of energy dissipation, and derive rigorous Grönwall-type inequalities in critical spaces. We further connect our results to the broader literature and provide a complete formal verification of all key estimates.