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CaffarelliKohnNirenberg

Scott Armstrong, Vlad Vicol

Palomar Registrypalomar/PALOMAR-2026-09-22-000003Sep 22, 2026math.APscore 0

A Lean 4 / Mathlib formalization of the Caffarelli-Kohn-Nirenberg partial regularity theory for suitable weak solutions of the three-dimensional incompressible Navier-Stokes equations with forcing in L^q, q > 5/2: the L^3 epsilon-regularity theorem (Theorem A), the gradient epsilon-regularity criterion (Theorem B) and the vanishing of the one-dimensional parabolic Hausdorff measure of the singular set (Theorem C). The three theorems are proved using only the standard axioms, restated together in a Mathlib-only comparator challenge and proved from the library theorems. The manuscript being…

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