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Global classical solutions of the “one and one-half” dimensional Vlasov-Maxwell-Fokker-Planck system. (English) Zbl 1332.35214
Commun. Math. Sci. 14, No. 1, 209-232 (2016); erratum ibid 15, No. 6, 1791-1799 (2017).
Summary: We study the “one and one-half” dimensional Vlasov-Maxwell-Fokker-Planck system and obtain the first results concerning well-posedness of solutions. Specifically, we prove the global-in-time existence and uniqueness in the large of classical solutions to the Cauchy problem and a gain in regularity of the distribution function in its momentum argument.

MSC:
35L60 First-order nonlinear hyperbolic equations
35Q83 Vlasov equations
82C22 Interacting particle systems in time-dependent statistical mechanics
82D10 Statistical mechanics of plasmas
35Q84 Fokker-Planck equations
35A09 Classical solutions to PDEs
Keywords:
kinetic theory
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