Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part I: Construction of Self-Similar Solutions with Admissible Stress and Flat Remainder
Year: 2026
Type: preprint
Abstract: This paper gives a readable and accessible version of the profile-construction part of OpenAI's manuscript "Finite Time Blowup for Navier-Stokes". We regard OpenAI's work as a major advance on the Navier-Stokes Millennium Prize Problem. The profiles are smooth and axi-symmetric. Inserting them into the Navier-Stokes equations gives a residual consisting of a divergence-form term and a remainder vanishing to infinite order in $1-t$ on fixed similarity sectors. The associated stress and radial shear satisfy the admissible cone condition. The stress need not be small. We introduce a new linear model that provides a clearer explanation of the inner core construction. The cancellation by oscillatory pulses will be treated in the companion paper "Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part II: Residual Correction via Oscillatory Pulses".
Source: arXiv (Cornell University)
Authors: Lei, Zhen, Ren, Xiao
Institution: Fudan University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214762479