论文标题
$ \ Mathbb r^3 $的Vlasov-Poisson的线性波动阻尼结构
Linearized wave-damping structure of Vlasov-Poisson in $\mathbb R^3$
论文作者
论文摘要
在本文中，我们研究了线性化的vlasov-Poisson方程，用于$ \ Mathbb r^3_x \ times \ times \ times \ mathbb r^3_v $中无限，同质的麦克斯韦背景分布的局部干扰。 In contrast with the confined case $\mathbb T^d _x \times \mathbb R_v ^d$, or the unconfined case $\mathbb R^d_x \times \mathbb R^d_v$ with screening, the dynamics of the disturbance are not scattering towards free transport as $t \to \pm \infty$: we show that the electric field decomposes into a very weakly-damped klein-gordon型进化，用于长波和兰道抑制的进化。 klein-gordon型波求解了领先顺序，尽管我们的模型是无碰撞的事实，但可压缩的Euler-Poisson方程线性地线性化，即在强局部局部或全局热效应，但在强局部分布功能没有趋势。我们证明了动态的克莱因 - 戈登部分的分散估计。电场的Landau阻尼部分的衰减速度比在高频下的较低频率和潮湿的潮湿速度快于自由运输。实际上，它以与筛选的情况相同的速度衰减。因此，对电场的贡献都不像真空案例一样行为。
In this paper we study the linearized Vlasov-Poisson equation for localized disturbances of an infinite, homogeneous Maxwellian background distribution in $\mathbb R^3_x \times \mathbb R^3_v$. In contrast with the confined case $\mathbb T^d _x \times \mathbb R_v ^d$, or the unconfined case $\mathbb R^d_x \times \mathbb R^d_v$ with screening, the dynamics of the disturbance are not scattering towards free transport as $t \to \pm \infty$: we show that the electric field decomposes into a very weakly-damped Klein-Gordon-type evolution for long waves and a Landau-damped evolution. The Klein-Gordon-type waves solve, to leading order, the compressible Euler-Poisson equations linearized about a constant density state, despite the fact that our model is collisionless, i.e. there is no trend to local or global thermalization of the distribution function in strong topologies. We prove dispersive estimates on the Klein-Gordon part of the dynamics. The Landau damping part of the electric field decays faster than free transport at low frequencies and damps as in the confined case at high frequencies; in fact, it decays at the same rate as in the screened case. As such, neither contribution to the electric field behaves as in the vacuum case.
