[On some limits in charged particle physics towards (magneto)hydrodynamic equations]
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.
Published online:
Yann Brenier 1; Norbert J. Mauser 2; Marjolaine Puel 3
@article{CRMATH_2002__334_3_239_0,
author = {Yann Brenier and Norbert J. Mauser and Marjolaine Puel},
title = {Sur quelques limites de la physique des particules charg\'ees vers la (magn\'eto)hydrodynamique},
journal = {Comptes Rendus. Math\'ematique},
pages = {239--244},
publisher = {Elsevier},
volume = {334},
number = {3},
year = {2002},
doi = {10.1016/S1631-073X(02)02206-9},
language = {fr},
}
TY - JOUR AU - Yann Brenier AU - Norbert J. Mauser AU - Marjolaine Puel TI - Sur quelques limites de la physique des particules chargées vers la (magnéto)hydrodynamique JO - Comptes Rendus. Mathématique PY - 2002 SP - 239 EP - 244 VL - 334 IS - 3 PB - Elsevier DO - 10.1016/S1631-073X(02)02206-9 LA - fr ID - CRMATH_2002__334_3_239_0 ER -
%0 Journal Article %A Yann Brenier %A Norbert J. Mauser %A Marjolaine Puel %T Sur quelques limites de la physique des particules chargées vers la (magnéto)hydrodynamique %J Comptes Rendus. Mathématique %D 2002 %P 239-244 %V 334 %N 3 %I Elsevier %R 10.1016/S1631-073X(02)02206-9 %G fr %F CRMATH_2002__334_3_239_0
Yann Brenier; Norbert J. Mauser; Marjolaine Puel. 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://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02206-9/
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