Uniform lifetime for classical solutions to the Hot, Magnetized, Relativistic Vlasov Maxwell system
Bibliographic record
Abstract
This article is devoted to the kinetic description in phase space of magnetically confined plasmas. It addresses the problem of stability near equilibria of the Relativistic Vlasov Maxwell system. We work under the Glassey-Strauss compactly supported momentum assumption on the density function \begin{document}$ f(t,\cdot) $\end{document} . Magnetically confined plasmas are characterized by the presence of a strong external magnetic field \begin{document}$ x \mapsto \epsilon^{-1} \mathbf{B}_e(x) $\end{document} , where \begin{document}$ \epsilon $\end{document} is a small parameter related to the inverse gyrofrequency of electrons. In comparison, the self consistent internal electromagnetic fields \begin{document}$ (E,B) $\end{document} are supposed to be small. In the non-magnetized setting, local \begin{document}$ C^1 $\end{document} -solutions do exist but do not exclude the possibility of blow up in finite time for large data. Consequently, in the strongly magnetized case, since \begin{document}$ \epsilon^{-1} $\end{document} is large, standard results predict that the lifetime \begin{document}$ T_\epsilon $\end{document} of solutions may shrink to zero when \begin{document}$ \epsilon $\end{document} goes to \begin{document}$ 0 $\end{document} . In this article, through field straightening, and a time averaging procedure we show a uniform lower bound ( \begin{document}$ 0 ) on the lifetime of solutions and uniform Sup-Norm estimates. Furthermore, a bootstrap argument shows \begin{document}$ f $\end{document} remains at a distance \begin{document}$ \epsilon $\end{document} from the linearized system, while the internal fields can differ by order 1 for well prepared initial data.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".