## Séminaire Orléans

**Long-time behavior of the Vlasov-Maxwell system**

Jonathan Ben-Artzi

Thursday 14 September 2023 14:00 - Orléans - Salle de Séminaires

**Résumé :**

The Vlasov-Maxwell system describes the behavior of a plasma subject to electromagnetic forces. The hyperbolic nature of Maxwell’s equations (finite speed of propagation of the electromagnetic fields) makes this system particularly difficult to analyze. Indeed, the global existence of solutions with large initial data is still an open problem, even after decades of research. Glassey and Strauss (CMP, 1987) proved the regularity of solutions with small initial data. In this talk I will present a recent result on the long-time behavior of these solutions: self-similar structure with explicit convergence rates. Consequently, one obtains the expected decay rate of $t^{-3}$ for the charge density. For plasmas that are globally neutral a better rate is obtained, suggesting that there is some damping mechanism. This is joint work with Stephen Pankavich.

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