Compressible Euler-Maxwell equations. (English) Zbl 1019.82023

Summary: The Euler-Maxwell equations as a hydrodynamic model of charge transport of semiconductors in an electromagnetic field are studied. The global approximate solutions to initial-boundary value problem are constructed by the fractional Godunov scheme. The uniform bound and \(H^{-1}\) compactness are proved. The approximate solutions are shown convergent by weak convergence methods. Then, with some new estimates due to the presence of electromagnetic fields, the existence of a global weak solution to the initial-boundary value problem is established for arbitrarily large initial data in \(L^\infty\).


82D37 Statistical mechanics of semiconductors
35Q35 PDEs in connection with fluid mechanics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
78A35 Motion of charged particles
82C70 Transport processes in time-dependent statistical mechanics
82D10 Statistical mechanics of plasmas
Full Text: DOI


[1] Alsunaidi, M. A. and El-Ghazaly, S. M. 1994.High frequency time domain modeling of GaAs FET’s using (the) hydrodynamic model coupled with Maxwell’s equations, 397–400. San Diego: IEEE Symp.
[2] DOI: 10.1109/22.506437
[3] DOI: 10.1109/T-ED.1970.16921
[4] Chen G.-Q., Acta Math. Sci. 6 pp 75– (1986)
[5] DOI: 10.1007/BF00916643 · Zbl 0864.76080
[6] Chen G.-Q., Modeling and Computation for Applications in Mathematics, Science, and Engineering pp 103– (1998)
[7] Chen G.-Q., Compressible Euler equations with general pressure law and related equations (1998)
[8] DOI: 10.1007/BF02102592 · Zbl 0858.76051
[9] DOI: 10.1007/s000000050096 · Zbl 0912.35131
[10] DOI: 10.1007/BF01206047 · Zbl 0533.76071
[11] DOI: 10.1109/43.68410 · Zbl 05447997
[12] Jerome J. W., Analysis of Charge Transport: A Mathematical Theory of Semiconductor Device (1996)
[13] DOI: 10.1002/(SICI)1097-0312(199606)49:6<599::AID-CPA2>3.0.CO;2-5 · Zbl 0853.76077
[14] DOI: 10.1007/BF02102014 · Zbl 0799.35151
[15] DOI: 10.1007/BF03167220 · Zbl 0797.76077
[16] DOI: 10.1007/978-3-7091-6961-2
[17] Rudan M., COMPEL 5 pp 149– (1986)
[18] Tartar L., Research Notes in Mathematics, Nonlinear Analysis and Mechanics 4 (1979)
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.