Boundary-Induced Symmetry Breaking in 3D Hydrodynamics: Intrinsic Spectral Smoothing of Navier-Stokes Fields via Non-Local Commutator Dynamics

We bypass the structural confinement of classical isotropic kernels to establish an uncoupled multi-dimensional fluid regularization. This formulation maps 3D velocity gradients as integrated responses to internal viscous distributions. The tool is simple. We inject the Riesz transform alongside an anti-symmetric Yukawa potential. Through spatial splitting over the domain, the boundary layer anomalies vanish. Dirac spikes collapse. Cross-term cancellation (τ - τ = 0) ensures this behavior at the solid interfaces. We prove that the resulting bi-harmonic dissipation framework Lc^2 * ν * ∇^4(u_i) builds an absolute energy cage within high-order Sobolev spaces. It smashes the convective velocity cascades that disrupt classical continuous models. The field possesses absolute uniqueness. It retains regular smoothness. Taking the vanishing scale limit verifies that the sequence contracts uniformly to the native local equations, opening a new window for continuum fluid synthesis.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-12
DOI
https://doi.org/10.5281/zenodo.22725320
Primary Topic
Navier-Stokes equation solutions
Type
article
Field-Weighted Citation Impact
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article

Boundary-Induced Symmetry Breaking in 3D Hydrodynamics: Intrinsic Spectral Smoothing of Navier-Stokes Fields via Non-Local Commutator Dynamics

Sami Mehennaoui
Zenodo (CERN European Organization for Nuclear Research)
Navier-Stokes equation solutions
article

Boundary-Induced Symmetry Breaking in 3D Hydrodynamics: Intrinsic Spectral Smoothing of Navier-Stokes Fields via Non-Local Commutator Dynamics

Sami Mehennaoui
article en

Abstract

We bypass the structural confinement of classical isotropic kernels to establish an uncoupled multi-dimensional fluid regularization. This formulation maps 3D velocity gradients as integrated responses to internal viscous distributions. The tool is simple. We inject the Riesz transform alongside an anti-symmetric Yukawa potential. Through spatial splitting over the domain, the boundary layer anomalies vanish. Dirac spikes collapse. Cross-term cancellation (τ - τ = 0) ensures this behavior at the solid interfaces. We prove that the resulting bi-harmonic dissipation framework Lc^2 * ν * ∇^4(u_i) builds an absolute energy cage within high-order Sobolev spaces. It smashes the convective velocity cascades that disrupt classical continuous models. The field possesses absolute uniqueness. It retains regular smoothness. Taking the vanishing scale limit verifies that the sequence contracts uniformly to the native local equations, opening a new window for continuum fluid synthesis.

Zenodo (CERN European Organization for Nuclear Research)
University of Skikda (DZ)
Sustainable cities and communities
Openalex Percentile: Top 6%
Navier-Stokes equation solutions
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