A Regularized Navier-Stokes Model with a Non-Local Gravitational Non-Collapse Principle

A Regularized Navier-Stokes Model with a Non-Local Gravitational Non-Collapse Principle Jorge Clavijo Hernández - ORCID: 0009-0001-3855-9593 - A Coruña, Spain - July 2026 ABSTRACT: From the empirical observation that nature does not generate infinite-energy vortices - from a swirl in a glass to a hurricane or a spiral galaxy - we conjecture a physical non-collapse principle. 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 when r→0. Building on Arnold's geodesic interpretation of Euler equations (1966) and Perelman's W-functional for Ricci flow (2002), we formulate a coupled system with a corrector term ε>0. We present formal monotonicity derivations for the combined functional Φ = W_NS + εG and numerical evidence in reduced 0D vorticity and 1D real Burgers-type non-local models showing gradient saturation and shock prevention for ε>0. Focus Note: This work does NOT claim to analytically solve the classical Navier-Stokes Millennium problem in its pure form. It proposes and studies a modified regularized system. Keywords: regularized Navier-Stokes, non-collapse principle, Perelman W-functional, Arnold geodesic flow, non-local model, Navier-Stokes regularization, entropy monotonicity License: CC-BY 4.0