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

From the empirical observation that Nature does not generate infinite-energy vortices — from the swirl in a glass to hurricanes or spiral galaxies — we conjecture a physical no-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, which diverges as 1/r.[u] 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 the coupling ε and regularization radius r0, 0D and 1D numerical evidence of saturation for ε>0 (Figures 1-2), and FFT-based O(N log N) methodology for 3D Taylor-Green validation (4π/|k|² kernel). This work does NOT claim to solve the Clay Millennium problem, which remains open. It proposes a physically motivated regularized system, analogous to Schrödinger-Newton and Vlasov-Poisson, with supplementary code for HPC validation. The conceptual framework is the author's own; computational formalization was assisted by Meta AI.