Incompressible Réthy Flows in Two Dimensions
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Bibliographic record
Abstract
This paper deals with the mathematical theory of a two-dimensional incompressible flow with two free boundaries effusing from a semi-infinite nozzle around a given obstacle, which is named the Réthy flows. The interesting and old problem was suggested and tried by M. Réthy in 1895 for a flow around a symmetric wedge. Here, we are concerned with the well-posedness theory of the symmetric Réthy flow with more general geometric conditions to the nozzle and obstacle. Given a mass flux at the inlet of the nozzle, we established the existence of the incompressible symmetric Réthy flows, containing two free boundaries behind the obstacle. Furthermore, the location estimate, the deflection angle estimate of the Réthy flow in the far field, and the asymptotic behavior of the Réthy flow in the upstream and downstream are also obtained. Finally, some results on the uniqueness of the Réthy flow are established.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 it