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.
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.
Publié le :
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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