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Pré-Publication, Document De Travail Année : 2023

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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Dates et versions

hal-04037563 , version 1 (20-03-2023)
hal-04037563 , version 2 (19-06-2023)

Identifiants

  • HAL Id : hal-04037563 , version 2

Citer

Christophe Cheverry, Slim Ibrahim. THE RELATIVISTIC VLASOV-MAXWELL SYSTEM: LOCAL SMOOTH SOLVABILITY FOR WEAK TOPOLOGIES. 2023. ⟨hal-04037563v2⟩
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