A direct same-scale closure route for the intrinsic Lie-profile frontier in 3D Navier--Stokes

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-03-23
DOI
https://doi.org/10.5281/zenodo.19240593
Primary Topic
Navier-Stokes equation solutions
Type
article
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article

A direct same-scale closure route for the intrinsic Lie-profile frontier in 3D Navier--Stokes

David Giannaccini
Zenodo (CERN European Organization for Nuclear Research)
Navier-Stokes equation solutions
article

A direct same-scale closure route for the intrinsic Lie-profile frontier in 3D Navier--Stokes

David Giannaccini
article en

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.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 5%
Navier-Stokes equation solutions
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A direct same-scale closure route for the intrinsic Lie-profile frontier in 3D Navier--Stokes — David Giannaccini · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS