Optimal three-ball inequalities and quantitative uniqueness for the Stokes system
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We study the local behavior of a solution to theStokes system with singular coefficients in $R^n$ with $n=2,3$. Oneof our main results is a bound on the vanishing order of anontrivial solution $u$ satisfying the Stokes system, which is aquantitative version of the strong unique continuation property for$u$. Different from the previous known results, our strong uniquecontinuation result only involves the velocity field $u$. Our proofrelies on some delicate Carleman-type estimates. We first use theseestimates to derive crucial optimal three-ball inequalitiesfor $u$. Taking advantage of the optimality, we then derive an upperbound on the vanishing order of any nontrivial solution $u$ to theStokes system from those three-ball inequalities. As an application,we derive a minimal decaying rate at infinity of any nontrivial $u$satisfying the Stokes equation under some a priori assumptions.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 |
| 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 it