Lower bound on the blow-up rate of the axisymmetric Navier-Stokes equations
Bibliographic record
Abstract
Journal Article Lower Bound on the Blow-up Rate of the Axisymmetric Navier–Stokes Equations Get access Chiun-Chuan Chen, Chiun-Chuan Chen 1Department of Mathematics and Taida Institute of Mathematical Sciences, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, Taiwan 106 and National Center for Theoretical Sciences, Taiwan, Taipei Office Correspondence to be sent to: ttsai@math.ubc.ca Search for other works by this author on: Oxford Academic Google Scholar Robert M. Strain, Robert M. Strain 2Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, USA Search for other works by this author on: Oxford Academic Google Scholar Horng-Tzer Yau, Horng-Tzer Yau 2Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, USA Search for other works by this author on: Oxford Academic Google Scholar Tai-Peng Tsai Tai-Peng Tsai 3Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada Search for other works by this author on: Oxford Academic Google Scholar International Mathematics Research Notices, Volume 2008, 2008, rnn016, https://doi.org/10.1093/imrn/rnn016 Published: 01 January 2008 Article history Received: 28 October 2007 Published: 01 January 2008 Revision received: 01 February 2008 Accepted: 05 February 2008
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.045 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.004 |
| Bibliometrics | 0.004 | 0.001 |
| Science and technology studies | 0.003 | 0.004 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.004 | 0.009 |
| Research integrity | 0.003 | 0.009 |
| Insufficient payload (model declined to judge) | 0.023 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".