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Stability of the relativistic Maxwellian in a collisional plasma. (English) Zbl 1113.82070
Summary: The relativistic Landau-Maxwell system is the most fundamental and complete model for describing the dynamics of a dilute collisional plasma in which particles interact through Coulombic collisions and through their self-consistent electromagnetic field. We construct the first global in time classical solutions. Our solutions are constructed in a periodic box and near the relativistic Maxwellian, the Jüttner solution.

MSC:
82D10 Statistical mechanics of plasmas
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
35Q60 PDEs in connection with optics and electromagnetic theory
35Q75 PDEs in connection with relativity and gravitational theory
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[1] Belyaev, S.T., Budker, G.I.: The Relativistic Kinetic Equation. Soviet Physics - Doklady. Proceedings of the Academy of Sciences of the USSR. 1, 218-222 (1956); Original (in Russian): Dokl. Acad. Nauk SSSR 107, 807 (1956); See also: Boltzmann?s equation for an electron gas in which collisions are infrequent, Plasma Physics and the problem of controlled thermonuclear reactions, Leontovich, M.A. (ed.), New York: Pergamon Press, 1961, pp. 431
[2] Desvillettes, L., Villani, C.: On the spatially homogeneous Landau equation for hard potentials. Part I: Existence, Uniqueness and Smoothness. Comm. PDE. 25(1-2), 179-259 (2000) · Zbl 0946.35109
[3] Glassey, R., Strauss, W.: Asymptotic Stability of the Relativistic Maxwellian. Publ. R.I.M.S. Kyoto Univ. 29, 301-347 (1993) · Zbl 0776.45008
[4] Glassey, R., Strauss, W.: Asymptotic Stability of the Relativistic Maxwellian via Fourteen Moments. Transport Theory and Statist. Phys. 24(4& 5), 657-678 (1995) · Zbl 0882.35123
[5] Guo, Y.: The Landau Equation in a Periodic Box. Commun. Math. Phys. 231, 391-434 (2002) · Zbl 1042.76053
[6] Guo, Y.: The Vlasov-Maxwell-Boltzmann System Near Maxwellians. Invent. Math. 153, 593-630 (2003) · Zbl 1029.82034
[7] Hinton, F.L.: Collisional Transport in Plasma. In: Handbook of Plasma Physics, Volume I: Basic Plasma Physics I, Rosenbluth, M.N., Sagdeev, R.Z. (eds.), Amsterdam: North-Holland Publishing Company, 1983, pp. 147
[8] Lemou, M.: Linearized Quantum and Relativistic Fokker-Plank-Landau Equations. Math. Meth. Appl. Sci. 23, 1093-1119 (2000) · Zbl 1018.82012
[9] Lifshitz, E.M., Pitaevskii, L.P.: Physical Kinetics; Landau and Lifshitz - Course of Theoretical Physics, Volume 10, Oxford: Oxford University Press, 1979
[10] Zhan, M.-Q.: Local Existence of Classical solutions to Landau equations. Transport Theory Statist. Phys. 23(4), 479-499 (1994) · Zbl 0810.35095
[11] Zhan, M.-Q.: Local Existence of solutions to the Landau-Maxwell system. Math. Methods Appl. Sci. 17(8), 613-641 (1994) · Zbl 0803.35114
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