A Conditional Physical-Closure Theorem for Three-Dimensional Navier-Stokes
Year: 2026
Type: preprint
Abstract: We apply the adequacy-residual calculus of Tsiokos2026XiCompanion and the layer-dissolving membrane endpoint of Tsiokos2026NeedleKiller to the smooth-data three-dimensional incompressible Navier--Stokes Cauchy problem. The argument fixes the Bradshaw--Grujic / Beale--Kato--Majda dissolving readout, measures the physical-native adequacy residual, and propagates it along the doubling Bradshaw--Grujic stages through the audited source-admission ledger. A no-go family rules out packing, sparseness, marker-only, and metric-shadow shortcuts; a Gevrey radius-window gate isolates the half-log endpoint obstruction; and a Littlewood--Paley transport map restores summable predictive propagation. Under the closure bundle and the typed-context discipline, every divergence-free initial datum in the accepted smooth-data channel therefore satisfies global existence. The same closure records are then recast as an AOR-instance membership witness for the smooth-data carrier, using the audit-closure meta-theory of Tsiokos2026AOR. This gives the audit-closed-carrier reading its record-level meaning inside the declared AOR discipline; the recasting is presented under the carrier-attached discharge-assignment discipline of the AOR meta-theory, and a data-bearing strengthening of the discharge-record fields is outside the present scope. We make no unconditional Clay--Millennium claim, no generic critical-Besov data claim, no criterion-native rewriting of the dissolving readout, and no claim of regularity independent of the audit records.
Author: Tsiokos, Ioannis
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165032879
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