zbMATH — the first resource for mathematics

A hierarchy of hydrodynamic models for plasmas zero-relaxation-time limits. (English) Zbl 0946.35074
A model hierarchy of hydrodynamic and quasihydrodynamic equations governing plasmas consisting of electrons and ions is considered. A rigorous proof is given of the zero relaxation time limits for hydrodynamic equations described by the Euler equations coupled with the linear or nonlinear Poisson equation. The basis of the proof involves high energy estimates for the Euler equations coupled with the use of compactness arguments.

35Q35 PDEs in connection with fluid mechanics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
82D10 Statistical mechanical studies of plasmas
Full Text: DOI
[1] Adams R.A., Sobolev Space (1981)
[2] G.Q. Chen, The theory of compensated compactness and the system of isentropic gas dynamics, preprint. MCS-P154-0590. 1990. Univ. of Chicago.
[3] DOI: 10.1002/cpa.3160470602 · Zbl 0806.35112 · doi:10.1002/cpa.3160470602
[4] DOI: 10.1016/0893-9659(94)00104-K · Zbl 0817.76102 · doi:10.1016/0893-9659(94)00104-K
[5] S. Cordier and E. Grenier, Quasineutral limit of Euler-Poisson system. preprint. 1996, LAN, Univ. Paris 6. · Zbl 0978.82086
[6] Cordier S., Mod. Math. Anal. Num. 32 pp 1– (1998)
[7] DOI: 10.1007/BF01206047 · Zbl 0533.76071 · doi:10.1007/BF01206047
[8] DOI: 10.1109/16.69922 · doi:10.1109/16.69922
[9] Th. Goudon, A. Jiingel and Y.J. Peng, Zero-electron-mass limits in hydrodynamic models for plasmas, Appl. Math. Letters, to appear.
[10] DOI: 10.1142/S0218202595000383 · Zbl 0833.76036 · doi:10.1142/S0218202595000383
[11] DOI: 10.1002/cpa.3160480303 · Zbl 0826.65078 · doi:10.1002/cpa.3160480303
[12] S. Junca and M. Rascle, Relaxation of the isothermal Euler-Poisson s>5- tem to the drift-diffusion equations. Quart. Appl. Math. to appear. · Zbl 1127.35354
[13] DOI: 10.1142/S0218202594000388 · Zbl 0820.35128 · doi:10.1142/S0218202594000388
[14] DOI: 10.1002/mana.3211850108 · Zbl 1157.35406 · doi:10.1002/mana.3211850108
[15] A. Jdngel and Y.J. Peng. A hierarchy of hydrodynamics models for plasmas : Zero-mass-electron limits. preprint. No. 98-1. 1998. LSlA. Univ. Blaise Pascal.
[16] DOI: 10.1002/(SICI)1097-0312(199606)49:6<599::AID-CPA2>3.0.CO;2-5 · Zbl 0853.76077 · doi:10.1002/(SICI)1097-0312(199606)49:6<599::AID-CPA2>3.0.CO;2-5
[17] DOI: 10.1007/BF02102014 · Zbl 0799.35151 · doi:10.1007/BF02102014
[18] DOI: 10.1007/BF01210707 · Zbl 0633.35049 · doi:10.1007/BF01210707
[19] Marcati P., Proc. Roy. Soc. Edinburgh Sect. A 125 pp 115– (1995)
[20] DOI: 10.1007/BF00379918 · Zbl 0829.35128 · doi:10.1007/BF00379918
[21] Murat F., Ann. Sc. Norm. Sup. Pisa. 5 pp 489– (1978)
[22] DOI: 10.1006/jmaa.1996.0081 · Zbl 0889.35109 · doi:10.1006/jmaa.1996.0081
[23] DOI: 10.1002/(SICI)1097-0312(199608)49:8<795::AID-CPA2>3.0.CO;2-3 · Zbl 0872.35064 · doi:10.1002/(SICI)1097-0312(199608)49:8<795::AID-CPA2>3.0.CO;2-3
[24] Y.J. Peng, Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for a nonlinear Euler-Poisson system. Nonlinear Analysis TMA, to appear. · Zbl 0965.65113
[25] DOI: 10.1006/jdeq.1995.1158 · Zbl 0845.35123 · doi:10.1006/jdeq.1995.1158
[26] Raviart P. A., A mathematical approach to electrostatic sheaths and plasma erosion. Lecture Notes of the Summer school in Ile d’014ron. France. pp 452– (1997)
[27] D. Serre, Relaxation semi-linkaire et cinktique des systkmes de lois de conservation, preprint, ENS-Lyon, No.228, 1998.
[28] Tartar, L. 1979.Compensated compactness and applications to partial differential equations, Research Note in mathematicsEdited by: Knops, R. J. 136–212. nonlinear analysis andmechanics, Heriot-Watt symposium,
[29] Singular perturbations of first order hyperbolic systems (1982)
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.