We prove propagation of $\frac{1}{s}$-Gevrey regularity $(s\in (0,1])$ for the Vlasov-Poisson system on ${\mathbb{T}}^d\times {\mathbb{R}}^d$ using a Fourier space method in analogy to the results proved for the 2D-Euler system in [20] and [23]. More precisely, we give quantitative estimates for the growth of the $\frac{1}{s}$-Gevrey norm and decay of the regularity radius for the solution of the system in terms of the force field and the volume of the support in the velocity variable of the distribution of matter. As an application, we show global existence of $\frac{1}{s}$-Gevrey solutions ($s\in (0,1)$) for the Vlasov-Poisson system in ${\mathbb{T}}^3\times {\mathbb{R}}^3$. Furthermore, the propagation of Gevrey regularity can be easily modified to obtain the same result in ${\mathbb{R}}^d\times {\mathbb{R}}^d$. In particular, this implies global existence of analytic $(s=1)$ and $\frac{1}{s}$-Gevrey solutions ($s\in (0,1)$) for the Vlasov-Poisson system in ${\mathbb{R}}^3\times {\mathbb{R}}^3$.

我们证明了 $\frac{1}{秒}$-Gevrey 规律 $(秒\in (0,1])$ 对于 Vlasov-Poisson 系统 ${\mathbb{吨}}^d\times {\mathbb{电阻}}^d$使用傅立叶空间方法类比 [20] 和 [23] 中为 2D-Euler 系统证明的结果。更准确地说，我们给出了对增长的定量估计$\frac{1}{秒}$-Gevrey 范数和规律性半径衰减，根据物质分布的速度变量中的力场和支撑体积来求解系统。作为一个应用程序，我们展示了全局存在$\frac{1}{秒}$-Gevrey 解决方案 ($秒\in (0,1)$) 对于 Vlasov-Poisson 系统 ${\mathbb{吨}}^3\times {\mathbb{电阻}}^3$. 此外，可以很容易地修改 Gevrey 正则性的传播以获得相同的结果${\mathbb{电阻}}^d\times {\mathbb{电阻}}^d$. 特别地，这意味着解析的全局存在$(秒=1)$ 和 $\frac{1}{秒}$-Gevrey 解决方案 ($秒\in (0,1)$) 对于 Vlasov-Poisson 系统 ${\mathbb{电阻}}^3\times {\mathbb{电阻}}^3$.