Sur quelques limites de la physique des particules chargées vers la (magnéto)hydrodynamique
[On some limits in charged particle physics towards (magneto)hydrodynamic equations]
Brenier, Yann1; Mauser, Norbert J.2; Puel, Marjolaine3
1 Laboratoire J.A. Dieudonné, Parc Valrose, 06100 Nice, France
2 Wolfgang Pauli Institute, c/o Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
3 Laboratoire d'analyse numérique, Université Pierre et Marie Curie, BC 187, 75252 Paris cedex 05, France
Comptes Rendus. Mathématique, Volume 334 (2002) no. 3, pp. 239-244.

We discuss the connection between different scalings limits of the quantum-relativistic Dirac–Maxwell system. In particular we give rigorous results for the quasi-neutral/non-relativistic limit of the Vlasov–Maxwell system: we obtain a magneto-hydro-dynamic system when we consider the magnetic field as a non-relativistic effect and we obtain the Euler equation when we see it as a relativistic effect. A mathematical key is the modulated energy method.

Nous discutons les connexions entre les modèles obtenus par différents « scalings » à partir du système de Dirac–Maxwell quantique-relativiste. En particulier, nous examinons des limites quasi-neutres/non-relativistes du système de Vlasov–Maxwell. Dans le cas d'un scaling où les effets relativistes sont partiellement conservés, on obtient un modèle du type magnéto-hydrodynamique (MHD), sinon on obtient les équations d'Euler des fluides incompressibles. Un point clef de notre analyse asymptotique rigoureuse est la méthode d'énergie modulée.

Received:
Published online:
DOI: 10.1016/S1631-073X(02)02206-9
Brenier, Yann 1; Mauser, Norbert J. 2; Puel, Marjolaine 3

1 Laboratoire J.A. Dieudonné, Parc Valrose, 06100 Nice, France
2 Wolfgang Pauli Institute, c/o Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
3 Laboratoire d'analyse numérique, Université Pierre et Marie Curie, BC 187, 75252 Paris cedex 05, France 
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     title = {Sur quelques limites de la physique des particules charg\'ees vers la (magn\'eto)hydrodynamique},
     journal = {Comptes Rendus. Math\'ematique},
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Brenier, Yann; Mauser, Norbert J.; Puel, Marjolaine. Sur quelques limites de la physique des particules chargées vers la (magnéto)hydrodynamique. Comptes Rendus. Mathématique, Volume 334 (2002) no. 3, pp. 239-244. doi : 10.1016/S1631-073X(02)02206-9. https://www.numdam.org/articles/10.1016/S1631-073X(02)02206-9/

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