Golse, F.; Saint-Raymond, L. The Vlasov-Poisson system with strong magnetic field in quasineutral regime. (English) Zbl 1053.82032 Math. Models Methods Appl. Sci. 13, No. 5, 661-714 (2003). Summary: Consider the motion of a gas of electrons with a background of ions, subject to the self-consistent electric field and to a constant external magnetic field. As the Debye length and the Larmor radius vanish at the same rate, the asymptotic current density is governed by the 2D1/2 incompressible Euler equation. Establishing limit requires to overcome various difficulties: compactness with respect to the space variable, control of large velocities, oscillations in the time variable. Yet, for particular initial data, the simultaneous gyrokinetic and quasineutral approximation is completely justified. Cited in 34 Documents MSC: 82D10 Statistical mechanics of plasmas 35F25 Initial value problems for nonlinear first-order PDEs 35L60 First-order nonlinear hyperbolic equations 35Q60 PDEs in connection with optics and electromagnetic theory 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 35Q99 Partial differential equations of mathematical physics and other areas of application Keywords:Vlasov-Poisson; quasineutral limit; Gyrokinetic approximation; relative entropy method; high frequency filtering PDFBibTeX XMLCite \textit{F. Golse} and \textit{L. Saint-Raymond}, Math. Models Methods Appl. Sci. 13, No. 5, 661--714 (2003; Zbl 1053.82032) Full Text: DOI References: [1] Arsen’ev A. A., Z. Vyčisl. Mat. Mat. Fiz. 15 pp 136– [2] Asano K., Stud. Math. Appl. 18 pp 369– [3] Babin A., Euro. J. Mech. 15 pp 291– [4] Babin A., Asympt. Anal. 15 pp 103– [5] Bouchut F., Series in Applied Math., in: Kinetic Equations and Asymptotic Theory (2000) [6] DOI: 10.1080/03605300008821529 · Zbl 0970.35110 · doi:10.1080/03605300008821529 [7] DOI: 10.1051/m2an:2000143 · Zbl 0954.76012 · doi:10.1051/m2an:2000143 [8] DOI: 10.1002/mma.1670080135 · Zbl 0619.35088 · doi:10.1002/mma.1670080135 [9] DOI: 10.1090/S0894-0347-1991-1102579-6 · doi:10.1090/S0894-0347-1991-1102579-6 [10] Desjardins B., Adv. Differential Equations 3 pp 715– [11] DOI: 10.1007/BF01206047 · Zbl 0533.76071 · doi:10.1007/BF01206047 [12] Frénod E., Asympt. Anal. 18 pp 193– [13] Frénod E., Math. Models Methods Appl. Sci. 10 pp 539– [14] DOI: 10.1016/S0021-7824(99)80002-6 · Zbl 1101.35330 · doi:10.1016/S0021-7824(99)80002-6 [15] DOI: 10.1006/jdeq.1998.3487 · Zbl 0921.35095 · doi:10.1006/jdeq.1998.3487 [16] DOI: 10.1016/S0021-7824(99)00021-5 · Zbl 0977.35108 · doi:10.1016/S0021-7824(99)00021-5 [17] Grad H., Proc. Symp. Appl. Math. pp 162– [18] 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 [19] DOI: 10.1080/03605309608821189 · Zbl 0849.35107 · doi:10.1080/03605309608821189 [20] DOI: 10.1006/jdeq.1999.3713 · Zbl 0958.35106 · doi:10.1006/jdeq.1999.3713 [21] Lifshitz E. M., Course of Theoretical Physics 10 (1981) · Zbl 0574.46011 [22] Lions P.-L., Oxford Lecture Series in Mathematics and its Applications 1, in: Mathematical Topics in Fluid Mechanics (1996) [23] DOI: 10.1007/s002050100144 · Zbl 0987.76088 · doi:10.1007/s002050100144 [24] DOI: 10.1142/S0218202500000641 · doi:10.1142/S0218202500000641 [25] DOI: 10.1006/jdeq.1994.1157 · Zbl 0838.35071 · doi:10.1006/jdeq.1994.1157 [26] Stein E., Singular Integrals and Differentiability Properties of Functions (1970) · Zbl 0207.13501 [27] Ukai S., Osaka J. Math. 15 pp 245– 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.