Applications of the Green Tensor Estimates of the Nonstationary Stokes System in the Half Space
Bibliographic record
Abstract
Abstract. In this paper, we present a series of applications of the pointwise estimates of the (unrestricted) Green tensor of the nonstationary Stokes system in the half space, established in our previous work [ Comm. Math. Phys., 399 (2023), pp. 1291–1372]. First, we show the [Formula: see text]-[Formula: see text] estimates for the Stokes flow with possibly nonsolenoidal [Formula: see text] initial data, generalizing the results of Giga, Matsui, and Shimizu [ Math. Z., 231 (1999), pp. 383–396] and Desch, Hieber, and Prüss [ J. Evol. Equ., 1 (2001), pp. 115–142]. Second, we construct mild solutions of the Navier–Stokes equations in the half space with mixed-type pointwise decay or with pointwise decay alongside boundary vanishing. Finally, we explore various coupled fluid systems in the half space including viscous resistive magnetohydrodynamic (MHD) equations, a coupled system for the flow and the magnetic field of MHD type, and the nematic liquid crystal flow. For each of these systems, we construct mild solutions in [Formula: see text], pointwise decay, and uniformly local [Formula: see text] spaces.
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.
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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".