Solving the Three-Dimensional Incompressible Navier–Stokes Global Regularity Problem by Structural Decomposition and Normalized Growth Analysis

This work addresses the three-dimensional incompressible Navier–Stokes global regularity problem through structural decomposition and normalized growth analysis. The analysis begins with the Navier–Stokes equations and follows the viscosity coefficient through successive structural decompositions. It then develops the vorticity and enstrophy identities, vortex-stretching structure, enstrophy-doubling intervals, and the Navier–Stokes scaling associated with those intervals. Each doubling interval is normalized from an enstrophy level Xn to 2Xn into a common passage from 1 to 2. Exact relations between consecutive normalized intervals are derived, together with weighted energy and time constraints. The resulting identities are then tested for whether they exclude a hypothetical finite maximal smooth time. The derived constraints remain mathematically compatible and do not produce the contradiction required to exclude finite-time singularity. Consequently, the proof developed here does not satisfy the Navier Global requirement.