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Global weak solutions of Vlasov-Maxwell systems. (English) Zbl 0698.35128
Using the method they developed in a previous paper to show global existence for the Cauchy problem for the Boltzmann equation, the authors are able to prove the existence of global weak solutions to the Vlasov- Maxwell system with no restriction on the size of initial data. The proof is basically in two steps. Firstly a weak stability theorem is demonstrated, based on a series of complex estimates. Next, global existence is established as an application of the previous result, going through a regularization procedure. The question of uniqueness is left open.
In the last section the authors mention several possible extensions of their theory, concerning different boundary value problems or various modifications of the governing differential equations.
Reviewer: A.Fasano

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
35D05 Existence of generalized solutions of PDE (MSC2000)
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