This paper is concerned with the asymptotic behavior of small data solutions to the three-dimensional Vlasov-Maxwell system in the exterior of a light cone. The plasma does not have to be neutral and no compact support assumptions are required on the data. In particular, the initial decay in the velocity variable of the particle density is optimal and we only require an $L^2$ bound on the electromagnetic field with no additional weight. We use vector field methods to derive improved decay estimates in null directions for the electromagnetic field, the particle density and their derivatives. In contrast with \cite{dim3}, where we studied the behavior of the solutions in the whole spacetime, the initial data have less decay and we do not need to modify the commutation vector fields of the relativistic transport operator. To control the solutions under these assumptions, we crucially use the strong decay satisfied by the particle density in the exterior of the light cone, null properties of the Vlasov equation and certain hierarchies in the energy norms.

中文翻译：

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光锥外部 Vlasov-Maxwell 系统解的渐近性质

本文关注的是光锥外部的三维 Vlasov-Maxwell 系统的小数据解的渐近行为。等离子体不必是中性的，并且不需要对数据进行紧致支撑假设。特别是，粒子密度的速度变量的初始衰减是最优的，我们只需要在电磁场上有一个 $L^2$ 边界，没有额外的权重。我们使用矢量场方法来推导出电磁场、粒子密度及其导数在零方向上的改进衰减估计。与 \cite{dim3} 相比，我们研究了整个时空的解的行为，初始数据的衰减较小，我们不需要修改相对论传输算子的交换向量场。