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Record W3048425551 · doi:10.2140/apde.2023.16.997

Finite-time blowup for a Navier–Stokes modelequation for the self-amplification of strain

2023· article· en· W3048425551 on OpenAlex

Why this work is in the frame

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affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueAnalysis & PDE · 2023
Typearticle
Languageen
FieldMathematics
TopicNavier-Stokes equation solutions
Canadian institutionsUniversity of British Columbia
FundersDivision of Mathematical SciencesUniversity of TorontoMcMaster UniversityNational Science Foundation
KeywordsEnstrophyMathematicsBurgers' equationNavier–Stokes equationsMathematical analysisPoisson's equationNon-dimensionalization and scaling of the Navier–Stokes equationsConstraint (computer-aided design)VortexPartial differential equationPhysicsVorticityMechanicsCompressibilityGeometry

Abstract

fetched live from OpenAlex

In this paper, we consider a model equation for the Navier--Stokes strain equation. This model equation has the same identity for enstrophy growth and a number of the same regularity criteria as the full Navier-Stokes strain equation, and is also an evolution equation on the same constraint space. We prove finite-time blowup for this model equation, which shows that the identity for enstrophy growth and the strain constraint space are not sufficient on their own to guarantee global regularity for Navier-Stokes. The mechanism for the finite-time blowup of this model equation is the self-amplification of strain, which is consistent with recent research suggesting that strain self-amplification, not vortex stretching, is the main mechanism behind the turbulent energy cascade. Because the strain self-amplification model equation is obtained by dropping certain terms from the full Navier-Stokes strain equation, we will also prove a conditional blowup result for the full Navier-Stokes equation involving a perturbative condition on the terms neglected in the model equation.

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Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Simulation or modeling · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.910
Threshold uncertainty score0.477

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.001
Bibliometrics0.0000.002
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.119
GPT teacher head0.381
Teacher spread0.263 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it