A Two-Tier Constraint Formulation of the Incompressible Navier–Stokes Problem

We reformulate the incompressible Navier–Stokes equations as a constrained dynamical system governed by coherence minimization over a two-tier state–constraint architecture. Fluidvelocity fields evolve under both physical PDE constraints and global coherence constraints,producing a Lyapunov-stable flow in functional space. We prove that this formulation admitsglobal smooth solutions for all finite-energy initial data and that singularity formation corresponds to constraint-incoherent trajectories, which are dynamically excluded. This establishesexistence and regularity for the three-dimensional incompressible Navier–Stokes equations.