Loeper, Grégoire Quasi-neutral limit of the Euler-Poisson and Euler-Monge-Ampère systems. (English) Zbl 1077.76072 Commun. Partial Differ. Equations 30, No. 8, 1141-1167 (2005). Summary: This paper studies the pressureless Euler-Poisson system and its fully nonlinear counterpart, the Euler-Monge-Ampère system, where the fully nonlinear Monge-Ampère equation substitutes for the linear Poisson equation. While the first is a model of plasma physics, the second is derived as a geometric approximation to the Euler incompressible equations. Using energy estimates, convergence of both systems to the Euler incompressible equations is proved. Cited in 20 Documents MSC: 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 35Q35 PDEs in connection with fluid mechanics 35Q60 PDEs in connection with optics and electromagnetic theory Keywords:quasi-neutral limit; Euler incompressible equations; energy estimates; convergence PDFBibTeX XMLCite \textit{G. Loeper}, Commun. Partial Differ. Equations 30, No. 8, 1141--1167 (2005; Zbl 1077.76072) Full Text: DOI arXiv References: [1] Alinhac S., Opérateurs Pseudo-Différentiels et Théoreme de Nash–Moser (1991) [2] Arnold V. I., Topological Methods in Hydrodynamics 125 (1998) · Zbl 0902.76001 [3] DOI: 10.1002/cpa.3160440402 · Zbl 0738.46011 · doi:10.1002/cpa.3160440402 [4] DOI: 10.1080/03605300008821529 · Zbl 0970.35110 · doi:10.1080/03605300008821529 [5] DOI: 10.1007/s002200000204 · Zbl 1025.82012 · doi:10.1007/s002200000204 [6] DOI: 10.1007/s00205-003-0291-4 · Zbl 1055.78003 · doi:10.1007/s00205-003-0291-4 [7] DOI: 10.1007/s00039-004-0488-1 · Zbl 1075.35046 · doi:10.1007/s00039-004-0488-1 [8] DOI: 10.2307/1971510 · Zbl 0704.35044 · doi:10.2307/1971510 [9] Chemin J.-Y, Asterisque 230 pp 177– (1995) [10] Cordero-Erausquin D., C R. Acad. Sci. Paris Ser. I Math. 329 pp 199– (1999) · Zbl 0942.28015 · doi:10.1016/S0764-4442(00)88593-6 [11] DOI: 10.1080/03605300008821542 · Zbl 0978.82086 · doi:10.1080/03605300008821542 [12] Cordier S., Methods Appl. Anal. 7 pp 391– (2000) [13] DOI: 10.2307/1971029 · Zbl 0373.76007 · doi:10.2307/1971029 [14] Gilbarg D., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 224, 2. ed. (1983) [15] DOI: 10.1016/S0021-7824(97)89959-X · Zbl 0885.35090 · doi:10.1016/S0021-7824(97)89959-X [16] DOI: 10.1002/(SICI)1097-0312(199709)50:9<821::AID-CPA2>3.0.CO;2-7 · Zbl 0884.35183 · doi:10.1002/(SICI)1097-0312(199709)50:9<821::AID-CPA2>3.0.CO;2-7 [17] DOI: 10.1007/s002200050388 · Zbl 0929.35112 · doi:10.1007/s002200050388 [18] DOI: 10.1002/cpa.3160350503 · Zbl 0478.76091 · doi:10.1002/cpa.3160350503 [19] Loeper , G. ( 2003 ). Applications de Vequation de Monge-Ampere a la Modelisation des Fluides et des Plasmas. These de doctorat. Universite de Nice-Sophia-Antipolis . [20] DOI: 10.1007/PL00001679 · Zbl 1011.58009 · doi:10.1007/PL00001679 [21] DOI: 10.1007/PL00004241 · doi:10.1007/PL00004241 [22] DOI: 10.1007/BF03167849 · Zbl 0717.35049 · doi:10.1007/BF03167849 [23] DOI: 10.1002/cpa.3160100103 · Zbl 0077.17401 · doi:10.1002/cpa.3160100103 [24] DOI: 10.1006/jdeq.1994.1157 · Zbl 0838.35071 · doi:10.1006/jdeq.1994.1157 [25] DOI: 10.1081/PDE-120030403 · Zbl 1140.35551 · doi:10.1081/PDE-120030403 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.