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Symmetric plasmas and their decay. (English) Zbl 0694.76049
Summary: Spherically symmetric global solutions are shown to exist for the relativistic Vlasov-Maxwell system of plasma physics. In view of a conjectured perturbation result concerning in particular “nearly” symmetric global solutions, we investigate the asymptotic properties of the symmetric solutions. In the case of only one particle species (say ions but no electrons) we get satisfactory decay estimates; in the general case (ions and electrons) we have preliminary results.

MSC:
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
82D10 Statistical mechanical studies of plasmas
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
35Q99 Partial differential equations of mathematical physics and other areas of application
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[1] Di Perna, R.J., Lions, P.L.: Global weak solutions of Vlasov-Maxwell systems. Preprint 1988
[2] Glassey, R.T., Schaeffer, J.: On symmetric solutions of the relativistic Vlasov-Poisson system. Commun. Math. Phys.101, 459–473 (1985) · Zbl 0582.35110 · doi:10.1007/BF01210740
[3] Glassey, R.T., Schaeffer J.: Global existence for the relativistic Vlasov-Maxwell system with nearly neutral initial data. Commun. Math. Phys.119, 353–384 (1988) · Zbl 0673.35070 · doi:10.1007/BF01218078
[4] Glassey, R.T., Strauss, W.A.: Singularity formation in a collisionless plasma could occur only at high velocities. Arch. Rat. Mech. Anal.92, 59–90 (1986) · Zbl 0595.35072 · doi:10.1007/BF00250732
[5] Glassey, R.T., Strauss, W.A.: Absence of shocks in an initially dilute collisionless plasma. Commun. Math. Phys.113, 191–208 (1987) · Zbl 0646.35072 · doi:10.1007/BF01223511
[6] Horst, E.: On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation I. Math. Meth. Appl. Sci.3, 229–248 (1981) · Zbl 0463.35071 · doi:10.1002/mma.1670030117
[7] Horst, E.: On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation II. Math. Meth. Appl. Sci.4, 19–32 (1982) · Zbl 0485.35079 · doi:10.1002/mma.1670040104
[8] Horst, E.: Global solutions of the relativistic Vlasov-Maxwell system of plasma physics. To appear in Dissertationes Mathematicae · Zbl 0725.35105
[9] Horst, E., Hunze, R.: Weak solutions of the initial value problem for the unmodified nonlinear Vlasov equation. Math. Meth. Appl. Sci.6, 262–279 (1984) · Zbl 0556.35022 · doi:10.1002/mma.1670060118
[10] Khil’mi, G.F.: Qualitative methods in the many body problem. New York: Gordon and Breach 1961
[11] Rein, G.: Forthcoming Ph. D. dissertation
[12] Schaeffer, J.: Global existence for the Poisson-Vlasov system with nearly symmetric data. J. Differ. Eqs.69, 111–148 (1987) · Zbl 0642.35058 · doi:10.1016/0022-0396(87)90105-7
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