Global Regularity of the Three-Dimensional Incompressible Navier-Stokes Equations

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Auteur principal: Asiryan, Valery
Format: Recurso digital
Publié: Zenodo 2025
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author Asiryan, Valery
author_facet Asiryan, Valery
contents <p>We consolidate six papers by the author into a self-contained program on the 3D incompressible Navier-Stokes equations. <br>Each part contributes a structural component that, taken together, closes a critical regularity mechanism and eliminates the minimal blow-up scenario. <br>Part I establishes Fourier cone-localized bounds for the Leray trilinear form, capturing anisotropic interactions at small angular apertures. <br>Part II proves a global angular-concentration flux inequality, controlling the transfer of kinetic energy through angularly concentrated packets. <br>Part III develops plate-localized angle depletion and a dyadic $2^{2j}$ scaling scheme, exhibiting quantitative depletion in near-coplanar interactions. <br>Part IV introduces a flux-dissipation decomposition that rigidifies inter-shell transfers and imposes a structural ban on adjacent-shell cascades. <br>Part V builds a critical-space minimal program, combining split absorption with conditional rigidity to preclude energy accumulation compatible with scaling. <br>Finally, Part VI implements hybrid angular splitting and frequency evacuation to derive band-local budget smallness for minimal critical configurations and to contradict the minimal blow-up scenario.</p>
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publishDate 2025
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spellingShingle Global Regularity of the Three-Dimensional Incompressible Navier-Stokes Equations
Asiryan, Valery
Navier-Stokes equations
Global regularity
Leray-Hopf solutions
Fourier cone localization
plate localization
angular depletion
flux-dissipation decomposition
energy cascade
critical spaces
minimal blow-up
backward uniqueness
ancient solutions
frequency evacuation
band-local energy budgets
angular splitting
conditional rigidity
harmonic analysis
<p>We consolidate six papers by the author into a self-contained program on the 3D incompressible Navier-Stokes equations. <br>Each part contributes a structural component that, taken together, closes a critical regularity mechanism and eliminates the minimal blow-up scenario. <br>Part I establishes Fourier cone-localized bounds for the Leray trilinear form, capturing anisotropic interactions at small angular apertures. <br>Part II proves a global angular-concentration flux inequality, controlling the transfer of kinetic energy through angularly concentrated packets. <br>Part III develops plate-localized angle depletion and a dyadic $2^{2j}$ scaling scheme, exhibiting quantitative depletion in near-coplanar interactions. <br>Part IV introduces a flux-dissipation decomposition that rigidifies inter-shell transfers and imposes a structural ban on adjacent-shell cascades. <br>Part V builds a critical-space minimal program, combining split absorption with conditional rigidity to preclude energy accumulation compatible with scaling. <br>Finally, Part VI implements hybrid angular splitting and frequency evacuation to derive band-local budget smallness for minimal critical configurations and to contradict the minimal blow-up scenario.</p>
title Global Regularity of the Three-Dimensional Incompressible Navier-Stokes Equations
topic Navier-Stokes equations
Global regularity
Leray-Hopf solutions
Fourier cone localization
plate localization
angular depletion
flux-dissipation decomposition
energy cascade
critical spaces
minimal blow-up
backward uniqueness
ancient solutions
frequency evacuation
band-local energy budgets
angular splitting
conditional rigidity
harmonic analysis
url https://doi.org/10.5281/zenodo.17602256