We study the asymptotic properties of the small data solutions of the Vlasov-Maxwell system in dimension three. No neutral hypothesis nor compact support assumptions are made on the data. In particular, the initial decay in the velocity variable is optimal. We use vector field methods to obtain sharp pointwise decay estimates in null directions on the electromagnetic field and its derivatives. For the Vlasov field and its derivatives, we obtain optimal pointwise decay estimates by a vector field method where the commutators are modification of those of the free relativistic transport equation. In order to control high velocities and to deal with non integrable source terms, we make fundamental use of the null structure of the system and of several hierarchies in the commuted equations.

中文翻译：

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具有小数据的 3d Vlasov-Maxwell 系统解的锐渐近行为

我们研究了 Vlasov-Maxwell 系统在第三维上的小数据解的渐近性质。没有对数据做出中性假设或紧凑支持假设。特别是，速度变量的初始衰减是最佳的。我们使用矢量场方法在电磁场及其导数的零方向上获得尖锐的逐点衰减估计。对于 Vlasov 场及其导数，我们通过向量场方法获得最佳逐点衰减估计，其中换向器是自由相对论输运方程的换向器的修改。为了控制高速和处理不可积的源项，我们从根本上利用了系统的零结构和交换方程中的几个层次结构。