Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part I: Construction of Self-Similar Solutions with Admissible Stress and Flat Remainder
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".
Related
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BibTeX
@misc{lei2026finitetime,
title = {{Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part I: Construction of Self-Similar Solutions with Admissible Stress and Flat Remainder}},
author = {Zhen Lei and Xiao Ren},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35406},
eprint = {2609.35406},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35406},
}
RIS
TY - UNPB
TI - Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part I: Construction of Self-Similar Solutions with Admissible Stress and Flat Remainder
AU - Zhen Lei
AU - Xiao Ren
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.35406
UR - https://arxiv.org/abs/2609.35406
AB - 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".
ER -