Abstract:We audit a finite-scale program for the local regularity problem of the three-dimensional incompressible Navier--Stokes equations. The program develops critical ledgers, coarse-grained defect decompositions, pressure--flux work identities, quotient cleanings, and bad-scale counting mechanisms. These results form an obstruction calculus: they locate how Caffarelli--Kohn--Nirenberg badness may be transported, hidden, or reproduced across scales, but they do not by themselves provide a coercive estimate excluding a surviving obstruction. We prove a resolution lemma separating full CKN badness into coarse badness and subfilter residual, and show that no unconditional single-scale domination by a signed combined-work detector is available. The audit therefore identifies the next necessary target: a filtered stretching--diffusion estimate, including subgrid forcing, leakage, pressure tails, and direction-incoherence defects, capable of converting the existing decomposition theory into a genuine regularity or obstruction-exclusion mechanism.
From: Runlong Yu [view email]
[v1]
Wed, 24 Jun 2026 03:13:24 UTC (24 KB)
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