Boundary-Induced Symmetry Breaking in 3D Hydrodynamics: Intrinsic Spectral Smoothing of Navier-Stokes Fields via Non-Local Commutator Dynamics
Year: 2026
Type: article
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.
Author: Mehennaoui, Sami
Institution: University of Skikda
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212357257
FWCI:
Cites:
Cited by:
Related to: