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Record W2963142957

4 KAM theory and the 3D Euler equation

2014· article· en· W2963142957 on OpenAlex

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fundA Canadian funder is recorded on the work.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

Venuenot available
Typearticle
Languageen
FieldMathematics
TopicMathematical Dynamics and Fractals
Canadian institutionsnot available
FundersEuropean Research CouncilNatural Sciences and Engineering Research Council of CanadaMinisterio de Economía y CompetitividadAgence Nationale de la Recherche
KeywordsMathematicsTorusManifold (fluid mechanics)Ergodic theoryInvariant (physics)Euler's formulaInvariant manifoldEuler characteristicEuler equationsClosed manifoldKolmogorov–Arnold–Moser theoremMathematical analysisFinsler manifoldDivergence (linguistics)Pure mathematicsMathematical physicsGeometryRicci curvature
DOInot available

Abstract

fetched live from OpenAlex

We prove that the dynamical system defined by the hydrodynamical Euler equation on any closed Riemannian 3-manifold M is not mixing in the Ck topology (k>4 and non-integer) for any prescribed value of helicity and sufficiently large values of energy. This can be regarded as a 3D version of Nadirashvili's and Shnirelman's theorems showing the existence of wandering solutions for the 2D Euler equation. Moreover, we obtain an obstruction for the mixing under the Euler flow of Ck-neighborhoods of divergence-free vectorfields on M. On the way we construct a family of functionals on the space of divergence-free C1 vectorfields on the manifold, which are integrals of motion of the 3D Euler equation. Given a vectorfield these functionals measure the part of the manifold foliated by ergodic invariant tori of fixed isotopy types. We use the KAM theory to establish some continuity properties of these functionals in the Ck-topology. This allows one to get a lower bound for the Ck-distance between a divergence-free vectorfield (in particular, a steady solution) and a trajectory of the Euler flow.

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 imitation

Not 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.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.002
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.957
Threshold uncertainty score0.523

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.028
GPT teacher head0.283
Teacher spread0.255 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Quick stats

Citations29
Published2014
Admission routes1
Has abstractyes

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