Noether’s theorems and conservation laws in magnetohydrodynamics and Chew–Goldberger–Low plasmas
Bibliographic record
Abstract
Abstract The ideal magnetohydrodynamic (MHD) equations and the ideal Chew–Goldberger–Low (CGL) plasma equations are studied using Lagrangian field theory methods. Action principles for the equations are developed and used to obtain conservation laws using Noether’s theorems. The Galilean group admitted by the equations leads to (i) energy, (ii) momentum, (iii) center of mass, and (iv) angular momentum conservation laws corresponding to the time translation, space translation, Galilean boosts, and rotational symmetries, respectively. The cross-helicity conservation law is a consequence of a fluid relabeling symmetry, and is local or non-local depending on whether the entropy gradient ( $$\nabla S$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>∇</mml:mi> <mml:mi>S</mml:mi> </mml:mrow> </mml:math> ) is perpendicular to the magnetic field induction $$\textbf{B}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>B</mml:mi> </mml:math> or otherwise. The point Lie symmetries of the MHD and CGL equations consist of Galilean transformations and scalings. Noether’s second theorem is used to derive a wave action conservation equation for a linear non-WKBJ Alfvén waves model for stellar winds. Recent symmetry group investigation of the Lagrangian MHD equations in two space dimensions are discussed.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".