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↑ 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∈ C∞. This gives a local solution of the three-dimensional incompressible Navier-Stokes equations with forcing f. Its velocity satisfies limsupt↑ 1|u(t)|L∞=∞. 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.
Related
- Finite-time blowup of the Euler equation without forcing
- Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part I: Construction of Self-Similar Solutions with Admissible Stress and Flat Remainder
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- A correction to the Zero Forcing Number of the Generalized Petersen Graphs P(n,3)
- Finite-time blowup for 2D unforced IPM
BibTeX
@misc{lei2026finitetime,
title = {{Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part II: Residual Correction via Oscillatory Pulses}},
author = {Zhen Lei and Xiao Ren},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06869},
eprint = {2611.06869},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06869},
}
RIS
TY - UNPB
TI - Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part II: Residual Correction via Oscillatory Pulses
AU - Zhen Lei
AU - Xiao Ren
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06869
UR - https://arxiv.org/abs/2611.06869
AB - 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↑ 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∈ C^∞. This gives a local solution of the three-dimensional incompressible Navier-Stokes equations with forcing f. Its velocity satisfies limsup_t↑ 1|u(t)|_L^∞=∞. 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.
ER -