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Generic global solutions of the relativistic Vlasov-Maxwell system of plasma physics. (English) Zbl 0722.35091

The time evolution of a collisionless plasma consisting of various species of particles which interact by selfconsistent, electromagnetic forces is described by the relativistic Vlasov-Maxwell system.
The author investigates the behaviour of classical solutions to the corresponding initial value problem under small perturbations of the initial data. First it is shown that the solutions depend continuously on the initial data with respect to various norms.
The main result is on global solutions. A global solution whose electromagnetic field decays in a certain way for large times is shown to remain global under small perturbations of the initial data and to retain the decay behaviour of the field. Therefore, such global solutions are generic.
This global perturbation result implies the existence of global classical solutions for small and for nearly neutral data - results which were known from the earlier work by R. Glassey and J. Schaeffer [Commun. Math. Phys. 119, No.3, 353-384 (1988; Zbl 0673.35070)] and R. Glassey and W. Strauss [ibid. 113, 191-208 (1987; Zbl 0646.35072)] and a new global existence result for nearly spherically symmetric initial data.
Reviewer: G.Rein

MSC:

35Q72 Other PDE from mechanics (MSC2000)
82D10 Statistical mechanics of plasmas
35B20 Perturbations in context of PDEs
35L15 Initial value problems for second-order hyperbolic equations
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