Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part II: Residual Correction via Oscillatory Pulses

Abstract

This paper is a companion to Part I: Construction of Self-Similar Solutions with Admissible Stress and Flat Remainder (arXiv:2609.35406). Part I constructs approximately self-similar flow profiles with a singular stress in divergence form. The associated velocity becomes unbounded as $t\uparrow 1$. Here, localized oscillatory pulses cancel this stress contribution through their averaged quadratic momentum flux. Successive corrections preserve the velocity growth and leave a smooth external force $f\in C^\infty$. This gives a local solution of the three-dimensional incompressible Navier-Stokes equations with forcing $f$. Its velocity satisfies $\limsup_{t\uparrow 1}\|u(t)\|_{L^\infty}=\infty$. Together, the two papers present a readable and accessible account of OpenAI's Finite Time Blowup for Navier-Stokes. We claim no original mathematical contribution.