Chaotic streaklines in new exact solutions to the Navier–Stokes equations
Bibliographic record
Abstract
Exact solutions to the Navier–Stokes equations with time-dependent viscosity ν(t) are constructed. The fluid velocities V(t,x) for these solutions are eigenvector fields for the operator curl. New exact solutions with ν(t)≤λ−2/t for t>t1, which describe dynamics of viscous fluid inside a ball and a spherical shell, have chaotic streaklines. For the derived solutions with ν(t)>ν1>0 or with ν(t)≥m/t, where m>λ−2 and t>t0, the length of each fluid streakline is finite and, therefore, its dynamics is not chaotic. As a consequence, it is shown that all Trkalian flows with constant viscosity ν=const are not chaotic.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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.
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 teacher head, 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".