论文标题
弗拉索夫 - 波森系统的Gevrey规律性
Gevrey regularity for the Vlasov-Poisson system
论文作者
论文摘要
我们证明了$ \ frac {1} {s} $ - gevrey juroparity $（s \ in（0,1））$ vlasov-poisson系统在$ \ mathbb {t}^d $上使用傅立叶空间方法对2D euler System in \ cite}和lo的结果证明的结果进行了类似方式，并使用傅立叶空间方法进行了类似。更准确地说，我们对$ \ frac {1} {s} $ - Gevrey Norm进行定量估计，以实力场和物质分布的速度变量中的梯度来解决系统的解决方案。作为一个应用程序，我们显示了$ \ frac {1} {1} {s} $ - gevrey solutions（$ s \ in（0,1）$）的$ \ mathbb {t}^3 $中的全局存在。此外，可以轻松地修改Gevrey规律性的传播，以在$ \ mathbb {r}^d $中获得相同的结果。特别是，这意味着分析$（s = 1）$和$ \ frac {1} {s} $ - gevrey solutions（$ s \ in（0,1）$）在$ \ mathbb {r}^3 $中。
We prove propagation of $\frac{1}{s}$-Gevrey regularity $(s\in(0,1))$ for the Vlasov-Poisson system on $\mathbb{T}^d$ using a Fourier space method in analogy to the results proved for the 2D Euler system in \cite{KV} and \cite{LO}. More precisely, we give a quantitative estimate for the growth in time of the $\frac{1}{s}$-Gevrey norm for the solution of the system in terms of the force field and the gradient 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 $\mathbb{T}^3$. Furthermore, the propagation of Gevrey regularity can be easily modified to obtain the same result in $\mathbb{R}^d$. 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 $\mathbb{R}^3$.
