Wollman, Stephen An existence and uniqueness theorem for the Vlasov-Maxwell system. (English) Zbl 0592.45010 Commun. Pure Appl. Math. 37, 457-462 (1984). The purpose of the present paper is to give a local existence and uniqueness theorem for the Vlasov-Maxwell system of equations, which is one of the fundamental sets of equations underlying the kinetic theory of plasma. It is a nonlinear integro-differential system which describes the collective motion of charged particles in the presence of their own self- generated electromagnetic field. Cited in 27 Documents MSC: 45K05 Integro-partial differential equations 78A35 Motion of charged particles 76X05 Ionized gas flow in electromagnetic fields; plasmic flow Keywords:local existence; uniqueness; Vlasov-Maxwell system; kinetic theory of plasma; nonlinear × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Cooper, J. Math. Anal. Appl. 75 pp 306– (1980) [2] Duniec, Bull. Acad. Polar. Sci. Ser. Sci. Tech. 21 pp 97– (1973) [3] Kato, Arch. Rational Mech. Anal. 58 pp 181– (1975) [4] Neunzert, Math. Meth. in the Appl. Sci. 2 pp 429– (1980) [5] Existence and uniqueness theory of the Vlasov equation, Technical Report MF-100, Magneto-Fluid Dynamics Division, Courant Institute, New York University, 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. 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.