Sur quelques limites de la physique des particules chargées vers la (magnéto)hydrodynamiqueOn 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. To cite this article: Y. Brenier et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 239–244.     

Aspects topologiques de la séparation dans les graphes infinis. I

Sans résumé     

Ein Maximumprinzip für nichtlineare parabolische Systeme

Ohne Zusammenfassung     

Zerlegung des vollständigen Graphen der Ordnungn in gewisse Fastlinearfaktoren

Ohne Zusammenfassung     

Generalized spherical harmonics and exterior differentiation in weighted sobolev spaces

We generalize spherical harmonics expansions of scalar functions to expansions of alternating differential forms (‘q-forms’). To this end we develop a calculus for the use of spherical co-ordinates for q-forms and determine the eigen-q-forms of the Beltrami-operator on S^N?1 which replace the classical spherical harmonics. We characterize and classify homogeneous q-forms u which satisfy Δu = 0 on ?^N??{0} and determine Fredholm properties, kernel and range of the exterior derivative d acting in weighted L^p-spaces of q-forms (generalizing results of McOwen for the scalar Laplacian). These techniques and results are necessary prerequisites for the discussion of the low-frequency behaviour in exterior boundary value problems for systems occurring in electromagnetism and isotropic elasticity.