A direct same-scale closure route for the intrinsic Lie-profile frontier in 3D Navier--Stokes
Year: 2026
Type: article
Abstract: We study the three-dimensional incompressible Navier--Stokes equations and their global regularity problem through a direct same-scale contradiction scheme on caloric lifts. The paper isolates an intrinsic Lie-profile frontier for ancient-core limits arising from a canonical tail-good restart sequence and develops a closure route that does not rely on a coarse-to-fine or cross-scale desynchronisation principle in the main argument. The central mechanism is: a nonzero intrinsic terminal Lie profile yields a fixed positive caloric slice on the limit; positive-time local caloric compactness transfers this lower bound to a persistent same-scale Lie witness along the restart sequence; a restart-scaled local caloric window estimate and tail-good linear smallness force every such fixed same-scale witness to vanish in the limit. This contradiction implies the vanishing of the intrinsic terminal Lie profile for every ancient-core limit. Auxiliary orbital, shell, and forcing-side reductions are retained only as supporting material. The presentation is organized so that the direct same-scale route is the mainline argument, while cross-scale packages are separated from the principal closure mechanism.
Author: Giannaccini, David
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7140591262
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