We introduce a geometric decoherence framework for the three-dimensional Navier-Stokes equations by formally establishing a structural analogy between multiplicative stochastic transport noise and the deterministic non-local pressure Hessian. While stochastic fluid models ensure global regularity through external noise that disrupts vorticity-strain alignment, we propose that the pressure Hessian -∇²p serves as an intrinsic, incompressibility-generated equivalent. Applying the Caffarelli-Kohn-Nirenberg partial regularity theorem to filter volume and surface blow-ups, we restrict our analysis to 1D filamentary singular sets. Using the exact Calderón-Zygmund kernel, we identify the resulting local restorative force. We execute a dimensional scaling analysis yielding a base decoherence exponent of δ ≈ 0.286, noting explicitly that reaching the critical sub-criticality threshold (δ > 0.5) requires an unproven Hardy-Littlewood-Sobolev exponent lift over the sparse set.
Tahir yamin (Tue,) studied this question.