Quasineutral limit of an Euler-Poisson system arising from plasma physics. (English) Zbl 0978.82086

Summary: We study the quasineutral limit of an Euler-Poisson system arising from plasma physics i.e. the limit when the Debye length tends to 0 of a nonlinear hyperbolic system coupled with a nonlinear elliptic equation. The proof uses pseudodifferential energy estimates techniques, in order to jutify classical limits in small time, for strong solutions.


82D10 Statistical mechanics of plasmas
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
35Q35 PDEs in connection with fluid mechanics
Full Text: DOI


[1] Alinhac S, Editions du Centre National de la Recherche Scientifique(CNRS) pp 190–
[2] Bony J.M, Ann. Sci. Ecole Norm. Sup 14 pp 209– (1981)
[3] Cordier S, Mathematical Modelling and Numerical Analysis 32 pp 1– (1998)
[4] S. Cordier, E. Grenier : Quasineutral limit of two species Euler Poisson system, in preparation · Zbl 0978.82086
[5] Decoster A, Ecole Polytechnique 32 (1994)
[6] Delcroix J.L, éditions du Centre National de la Recherche Scientifique (CNRS)
[7] DOI: 10.1002/(SICI)1097-0312(199709)50:9<821::AID-CPA2>3.0.CO;2-7 · Zbl 0884.35183
[8] Grenier E, Séminaire sur les équations aux Dérivées Partielles 21 pp 13– (1995)
[9] Hörmander L, Grundlehren der Mathematischen Wissenschaften 275 (1994)
[10] Krall, N and Trivelpiece, A. 1986. ”Principles of plasma physics”. San francisco press.
[11] Majda A, Applied Mathematical Science 53 (1984)
[12] Robert A, Progress in Mathematics (1987)
[13] Taylor M, Progress in 100 (1991)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.