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## On the non-relativistic limit of Vlasov-Maxwell

In this note, I briefly explain my recent joint work with D. Han-Kwan (CNRS, Ecole polytechnique) and F. Rousset (Paris-Sud) on the non-relativistic limit of Vlassov-Maxwell. Precisely, we consider the relativistic Vlasov-Maxwell system, modeling the dynamics of electrons with electron density distribution ${f(t,x,v)}$, which reads

$\displaystyle \partial_t f + \hat v \cdot \nabla_x f + (E + \epsilon \hat v \times B)\cdot \nabla_v f = 0$

on ${\mathbb{T}^3\times \mathbb{R}^3}$, with the relativistic velocity ${\hat v = v/\sqrt{1+ \epsilon^2 |v|^2}}$.