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Global weak solutions of Vlasov‐Maxwell systems
Author(s) -
Diperna R. J.,
Lions P. L.
Publication year - 1989
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160420603
Subject(s) - mathematics , stability (learning theory) , vlasov equation , work (physics) , maxwell's equations , renormalization , mathematical analysis , mathematical physics , physics , plasma , computer science , quantum mechanics , machine learning
We study here the Vlasov‐Maxwell system in its classical and relativistic form. We prove the stability of solutions in weak topologies and deduce from this stability result the global existence of a weak solution with large initial data. The main tools consist of a new regularity result for velocity averages of solutions of some general linear transport equations and the method of renormalization introduced by the authors in previous work.