论文标题
绿色的功能和一维Vlasov-Maxwell-Boltzmann系统的尖锐行为
Green's function and Pointwise Behavior of the One-Dimensional Vlasov-Maxwell-Boltzmann System
论文作者
论文摘要
本文研究了一维Vlasov-Maxwell-Boltzmann（VMB）系统的绿色功能的点时空行为。结果表明，绿色的功能由宏观扩散波和huygens波浪组成，速度$ \ pm \ pm \ sqrt {5/3} $在低频时，具有高速$ \ pm 1 $的夸张波在高频率下，高频率，单次的动力学和短暂的短波和剩余时间和剩余时间和剩余时间和剩余时间和差异时间和差异。请注意，这些高频双曲波是全新的，无法观察到Boltzmann方程和Vlasov-Poisson-Boltzmann系统。此外，我们基于绿色的功能，建立了非线性VMB系统全局解决方案的点上时时间估计。与Boltzmann方程和Vlasov-Poisson-Boltzmann系统相比，引入了一些新想法，以克服粒子运输和电磁场的旋转效应以及新的双曲线波和新的双波波和奇异的引导短波引起的困难。
The pointwise space-time behavior of the Green's function of the one-dimensional Vlasov-Maxwell-Boltzmann (VMB) system is studied in this paper. It is shown that the Green's function consists of the macroscopic diffusive waves and Huygens waves with the speed $\pm \sqrt{5/3}$ at low-frequency, the hyperbolic waves with the speed $\pm 1$ at high-frequency, the singular kinetic and leading short waves, and the remaining term decaying exponentially in space and time. Note that these high-frequency hyperbolic waves are completely new and can not be observed for the Boltzmann equation and the Vlasov-Poisson-Boltzmann system. In addition, we establish the pointwise space-time estimate of the global solution to the nonlinear VMB system based on the Green's function. Compared to the Boltzmann equation and the Vlasov-Poisson-Boltzmann system, some new ideas are introduced to overcome the difficulties caused by the coupling effects of the transport of particles and the rotating of electro-magnetic fields, and investigate the new hyperbolic waves and singular leading short waves.
