Grenier, Emmanuel Oscillations in quasineutral plasmas. (English) Zbl 0849.35107 Commun. Partial Differ. Equations 21, No. 3-4, 363-394 (1996). Summary: The purpose of this article is to describe the limit, as the vacuum electric permittivity goes to zero, of a plasma physics system, deduced from the Vlasov-Poisson system for special initial data (distribution functions which are analytic in the space variable, with compact support in velocity), a limit also called “quasineutral regime” of the plasma, and the related oscillations of the electric field, with high frequency in time. Cited in 1 ReviewCited in 44 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 76X05 Ionized gas flow in electromagnetic fields; plasmic flow Keywords:quasineutral regime of the plasma; plasma physics; Vlasov-Poisson system PDF BibTeX XML Cite \textit{E. Grenier}, Commun. Partial Differ. Equations 21, No. 3--4, 363--394 (1996; Zbl 0849.35107) Full Text: DOI References: [1] Alinhac, S. Approximation et temps de vie des solutions des equations d’Euler isentropiques en dimension 2 d’espace, · Zbl 0743.76061 [2] Alinhac S., Invent, math. n{\(\deg\)}III pp 627– (1993) · Zbl 0798.35129 [3] Bardos C,, Ann. Inst. Henri. Poincare, Anal non lineaire pp lOl– (1985) [4] Benachour S., Scuola. Norm. Sup. Pisa Cl.Sci 16 (4) pp 83– (1989) [5] Berk H. L., experimental and computational Observations Phys. of Fluids 13 (4) pp 980– (1967) [6] Bensoussan A., Studies in Math, and its applications, (1978) [7] Y. Brenier : A Vlasov–Poisson type formulation of the Euler equations, rapport INRIA 1070 (1989). [8] Brenier Y, J. Amer. Math. Soc. 2 pp 225– (1990) [9] Brenier Y, le cas indkpendant du temps, C. R. Acad. Sci. Paris Soc. I Math. 318 pp 121– (1994) [10] Browning G., Siam J. Appl. Math. 42 (1982) pp 704– [11] Caflisch R., Bull. Amer. Math. Soc. 23 (2) pp 495– (1990) · Zbl 0723.35003 [12] Ebin D.G., Comm. Pure Appl. Math. 35 pp 451– (1982) · Zbl 0478.76011 [13] E. Grenier : Defect measures of the Vlasov–Poisson system in the quasineutral regime, to appear in Comm. Partial Diferential Equations. · Zbl 0828.35106 [14] Klainerman, S., Comm. Pure Appl. Math. 35 pp 629– (1982) · Zbl 0478.76091 [15] J.–L. Lions : Perturbations singulikres, Lectures Notes in Mathematics, 323, Springer–Verlag, 1973. [16] P.–L. Lions : Limites incompressible et acoustique pour des fluides visqueux, compressibles et isentropiques, C. R. Acad. Sci. Paris Sér. I Math. t317 (1993) p1197 – 1202. · Zbl 0795.76068 [17] Pfaffelmoser K., J. Differential Equations 95 pp 281– (1992) · Zbl 0810.35089 [18] Sideris T, Indiana Univ. Math. J. 40 pp 535– (1991) · Zbl 0736.35087 [19] Ukai S., equation, Osaka J. Math. 15 pp 245– (1978) [20] Ukai S, J. Math. Kyoto Univ , 26 pp 497– (1986) · Zbl 0618.76074 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.