Physical Evidence for a Non-Local Gravitational No-Collapse Regularization of Navier-Stokes: 0D and 1D Models with FFT Methodology for 3D

Abstract

From the empirical observation that nature does not generate infinite-energy vortices — from a swirl in a glass to hurricanes or spiral galaxies — we conjecture a physical non-collapse principle: no physical system can reach infinite energy density without paying a gravitational cost. We propose a regularized Navier-Stokes system where concentrated kinetic energy pays a non-local cost G=∫∫|u(x)|²|u(y)|²/|x-y| dx dy, diverging as 1/r. Building on Arnold's geodesic interpretation (1966) and Perelman's W-entropy (2002), we study ∂t u + (u·∇)u = -∇p + νΔu - ε u(x) ∫|u(y)|²/|x-y| dy, div u=0. We provide dimensional analysis of ε and regularization radius r0, 0D and 1D numerical evidence of saturation for ε>0 (Figs 1-2), and O(N log N) FFT methodology for 3D Taylor-Green validation (kernel 4π/|k|²). New in v2: Added Figure 3 with real 3D pseudo-spectral execution N=32³ (Taylor-Green, ν=0.02) showing 10-12% reduction of max|∇u| with non-local term. Full high-Re validation (N≥256³) left for future HPC. This work does NOT claim to solve the Clay Millennium problem, which remains open. It proposes a physically grounded regularized system analogous to Schrödinger-Newton and Vlasov-Poisson. Conceptual framework by the author; computational formalization assisted by Meta AI.