THE RELATIVISTIC VLASOV-MAXWELL SYSTEM
Résumé
This article is devoted to the Relativistic Vlasov-Maxwell system in space dimension
three. We prove the local existence and uniqueness of solutions for initial data
(f_0,E_0,B_0) in L^\infty \times H^1 \times H^1, with f_0 compactly supported in momentum. This result is the consequence of the local smooth solvability for the preceding ``weak" topology. It is derived from a representation formula decoding
how the momentum spreads and revealing that the domain of influence in momentum is controlled by mild information (involving only conserved quantities).
We do so by developing a Radon Fourier analysis on the RVM system, leading to
the study of a class of singular weighted integrals. In parallel, we implement our method to construct smooth solutions to the RVM system in the regime of dense, hot and strongly magnetized plasmas.
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