Incompressible flow around thin obstacle, uniqueness for the wortex-wave system
Bibliographic record
Abstract
We present here the results concerning the influence of a thin obstacle on the behavior of incompressible flow. We extend the works made by Itimie, Lopes Filho, Nussenzveig Lopes and Kelliher where they consider that the obstacle shrinks to a point. We begin by working in two-dimension, and thanks to complex analysis we treat the case of ideal and viscous flows around a curve. Next, we consider three-dimensional viscous flow in the exterior of a surface/curve. We finish by giving uniqueness of the vortex-wave system with a single point vortex introduced by Marchioro and Pulvirenti, in the case where the initial vorticity is constant near the point vortex. This last result gives, in particular, the uniqueness of the limit system obtained in the case of a perfect fluid around a point. We choose here to give the main steps of this uniqueness result, obtained in collaboration with E. Miot.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".