Global Regularity of 3D Incompressible Navier-Stokes Equations via Deterministic Harmonic Resolution

Barry L. Guevremont

Global Regularity of 3D Incompressible Navier-Stokes Equations via Deterministic Harmonic Resolution

For any smooth, divergence-free initial velocity field uu2080 ∈ Hˢ(ℝ³) with s ≥ 1/2, there exists a unique, global-in-time smooth solution u(x, t). We prove this by establishing that the Leray-Hopf energy inequality is a strict equality and that the velocity gradient satisfies a uniform L∞ bound for all t ≥ 0. This closes the supercritical scaling gap and satisfies the Beale—Kato—Majda criterion, thereby proving global regularity of the 3D incompressible Navier-Stokes equations.

Comments: Corrected version with fixed Lean 4 code, added images (coffee_cup.png and math_monster.jpg), and minor formatting improvements. 10 pages. Physics - Mathematical Physics category.

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[v1] 2026-03-11 20:33:28
[v2] 2026-03-21 02:59:08

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