Mathematical Physics

   

Global Existence and Smoothness of The Navier-Stokes Equation via Spectral Decimation on Icosahedral Manifolds

Authors: Stephen Ryan Moorehead-McDaniel

Since the original formulation of the Navier-Stokes equations in 1822, the inability to prove global regularity has been fundamentally rooted in a physical misconception: the assumption that the fluid continuum is isotropic at the dissipation scale. We assert that the Millennium Prize problem, as currently posed, is unsolvable not due to a lack of mathematical tools, but due to an incomplete understanding of the physical vacuum. This paper does not introduce a new external rule; rather, it identifies an intrinsic Topological Boundary Constraint that has always governed fluid dynamics but remained unobserved by standard analysis. We demonstrate that the vacuum naturally selects the Gamma_{120} manifold (derived from the symmetry of the Great Rhombicosidodecahedron) as the global attractor for energy dissipation. By observing the inherent 72^circ torsional alignment of the vorticity field, we show that the non-linear advection term is geometrically depleted at the Kolmogorov scale, naturally precluding singularity formation. Finally, we show that the standard isotropic model violates the Second Law of Thermodynamics via spectral aliasing, a violation that nature corrects through this pre-existing geometric governor. The solution is smooth because the physical universe does not permit the isotropic blow-up assumed by the mathematical model.

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[v1] 2025-12-27 01:16:37

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